Workshop on Low-Dimensional Quantum Workshop on Low ......Workshop on Low-Dimensional Quantum Field...
298
INSTITUTE FOR NUCLEAR STUDY UNIVERSITY OF TOKYO INS -JT-493 Tanashi, Tokyo 188 February 1990 Japan Workshop on Low-Dimensional Quantum Field Theory and its Applications -Collected Transparencies of the Talks- Institute for Nuclear Study, University of Tokyo December 18-20 1989 Edited by H. Yamamoto INSTITUTE FORNUCLEARSTUDY UNIVERSITY OFTOKYO Tanashi , Tokyo188 Japan INS- T -493 February 1990 Workshop on Low-DimensionalQuantum Field Theory and its App 1i cations -Collected Tr ansparenciesof the Ta lks ・ InstituteforNuclearStudy , Universityof Tokyo December18 ・ 201989 Edited by H.Yamamoto
Workshop on Low-Dimensional Quantum Workshop on Low ......Workshop on Low-Dimensional Quantum Field Theory and its Applications December 18 - 20, 1989 Sponsored by Institute for Nuclear
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10:00-10:45 ()
10:0010:55 ()
Oimensions
Term
1455-16:15 ()
10:00-10:35 ()
10:40-11:50 ()
14:55-15:40 ()
Hubbard Model Approach
( K x ) 87
Quantized Hall liffect of Perfect Crys ta ls in Two
Dimensions
) 107
T h e o r y of E l e c t r o n i c D i a m a g n e t s m in T w o -
D i m e n s i o n a l L a t t i c e s
. (!«AftttW) Induced C hern -Simons Jl
1 3 5
Anyons and Q u a n t u m T h e o r i e s w i t h C h e r n - S i m
o n s T e r m
151
169
Mill**? ('kkm 187
RVB IK 1 j >j 'r :w* y TJ] >\sa i/ * j . is— -y 3 v
' I 'RIliliai C r f f i K A n 205
Chiral Spin S la te s in Extended t - J Model
^fti/t^~-ffi CMkmm) 239
-mm-k (*A;ftfS) 249 Bose -Fermi Transmutaton COSH^WIXtSl1
&mrr, (HACPB r.) 271
irt • r- +- - ^ a a i 14\m f'. •> y-7^fj
*_h.& (OiAft*) 28i
2 9 1
IF1QHEGLPIl
[1¥ Ha ldane i-
111M()..... … -…… ... … ………… …………......… 97
Quant lzed Hall E ffect of Perfect Crystals in Two Dimensions
ft1J (;1t'l:) h .......................H .. …………… …u …...H ..……
107
Theory of Eletroni c Diamagnetsm in Two-D i mens i ona 1 L a t t i
ces
Id:.()… - …… ...H ……………………H H H .........H 119
1nduced Chern -Simons
Anyons and Quantum Theories wi th CherSimonsTerm
(>;';) ..... …................• . • . • • . . • . • • . . 0 ....
…........……… 151
r11{ι
(;It:f'n
187
[1 g~IJ iI\kif: ('j::U ‘ ….... ω u …………………..… … 205
Chi ral Spin S lates in Extended t -J Model
() …… … .... 0 … …‘ … … H H 239
f!llhhard ~10de 1 p~ "pproach
'ffli (!U) .••••• ••• ..... ……… - … ......H ....…….... 249
l30se -Ferm i Transmutaton
1.¥ (- J*JI γ 7I
il<J-. C!U;)…… ….. …-…… -……… …...........H -…………....…...H
281
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6
5
c rY
=70 mK
ETL (S ta) ( NP L ( VS L (
LCIE(7
1/
10
G = G a A s / A 1 xG a l-xA s (x=O.3)
a:!2S1(Lab).!2SI(Lab)
c:!2SI(ETL).!2SI (E T L)(?)
e : 1 !2 BIPM( t ())=1 !2SI-(! .516-0.0554(t-1985))μQ !2BIPM!2SI.
(0.1-O.lppm)
:S=Si-MOSFET
~ I.IT. WTM' T1 )
o N9-8H53 (e 2 /4h)
72-17H53(eY8h) • 72-17H53 (eι/4h)
F-J 11
133 10 20
ISD (μ'A)
'(osJi J..i .. t.l. : Plty' /a".. 9 3.1 (J 'i ") "'/1‘
1 4 15 0.38 4 10.5 0.38 . 4 10.5 1.36
/
"XV
\ free electron
V n(
Fig. 1. Definition of "slope". In this paper we define the inclined
Hall plateau as: slope=(d/7x//dK l)QHE/ (d/»v/dKg)ra, at the value
of Vt where pxx drops to a minimum, p£n, under the quantum Hall
effect (QHE) regime.
Joji KINOSHITA et al. llitt ? 2«.it 1 SflM
10'
, . . . I 10 100 1000
IS D ("A) Fig. 4. (slope)"1 and cr£j* as functions of Ii0.
10"
-f Q-hh 4iZZJC-uf"
Joji KINOSHITA tt 0/. (' '" ) 2...1 1 sQ f1
1O6
1O7
ω
l - M l
0V tfp.r 7.U o
--- 7.12. 1O
100 1000 ISD (nA)
vgn s
Fig. 1. Definition of“s)ope". In this paper we define the inclined
Hall plateau as: slope=(dpxyl d V.)QHEI (dp. !dV.).at the value of
Y. wherc Pxx drops to a minimumρ;;n undcr thc quantum Hall etfect
(QHE) regime.
Quantized Hall Resistance
von Klitzing constant:
Fine structure constant a :
?
Fig. 1 Comparison of the measured values for the von Klitzing con-
stant at the PTB (*) with values measured at various other
institutes (o), which are given in the report of the 1987
international com- parison of 1-n-restsUnces. AH data were measured
in terms of the as-maintained unit and converted to «69-BI
(1987-10-20) using this international comparison. The dashed line
is the weighted man value ftKof»\l data except PTB's. PTB *-«n-t'T
-»*rjfr- L t / V » ;
BIPM
CSIRO
ETl
M
lClE
NBS
NIM
NPl
NRC
VSl
0fM
-i
Resistanoe
10x(~ 1 )- "K
Fig. 1 Comp:uison of tht; measured values for the von Klitzing con-
stant at the PTB ()with nlues measured at v:uious other institutes
(0) which :ue giYen there tof the 1987 international com- p:uison
of l-n-resistances. Adatawere measured in terms of the
as-maintained unit dc .vertedto n69-Bl (198710-20)using this
ternationalcomparisonda1ineis the we.tedman va1ue
RJC ofaUωta except PTB's PTfjt '''1
0.800 0.802 I I I I
0,804
[(flK/25 812.8 Q)-1Jx106
0,000 0.100 0.200 0,300 0.400 0,500 0.6&
I(HK/25 812.8 n ) - 1 ] x 1 0
?
RK-25 812 0 (0).
0 0 0M 0806 0 0810 0012 0814
5 .. lH) .. CSIRO/G.l.I. -
N8Sα'pRH)t . ' l10)
0..2¥111 H l'V
N8S lo;
F1g.A1 . • -CSlRO l1)
00∞ 01∞ 02∞ 0300 04∞ 05∞ 0
[(RK/258128 Q)1)x 10 6
.".CaI......"K-aMnToI.τeaI rai.w';;
/μ~' .. u\~ o('t r~~ l r ~.- ¥''1". h)
-I ~ln _1 f.' .2.(l t.\~ ci ('RH)al----E77)
""lfl ¥ ~U. R 'i'J
012 0'14
R g R.CI)
source standard cell potentiometer
Tig. 1. Sehuutlc diagram of tba quantlxad Hall nilacanc* Btaaurlng
apparatua.
2
L_ JL-_.J 150 & Si-MO~FET source
standard celt L~ L___ potentiometer
F11' 1. SehUcd1alr.. of tha 'l"U.zadlIal.l.
raa11>1appratu.
oII CO
-"-.
- n H M
a O
A H 3
R. R. (+) + R. 15.7 15.8 15.9 16.0 R.. R... (+) + R. VG(V) R.
)¥(T)/2 R G'f~3. 2 .n. R.u
\1*1. 5-JO
Sources of uncertainty
Realization of "SI-NML Transport of CSIRO 1-fl resistors Comparison
of 1-fl resistor with CSIRO 1-fl resistors Temperature fluctuation
of 1-fl resistor Drift of 1-fl resistor Comparison of 6453.2-fl
resistor, RR, with 1-fl resistor Comparison of quantized Hall
resistance with RR
Total (RSS)
0.01
Rea 1 fzat1 on . of B ~p
OsI Trans ofIRO B 0.01 2 1-0 sis rs
Csptartson of 14 A 0.017 3 stor w1th CSIRO B 0.009 4
1-0 res1sto
1-0 resistor
stor II
B 0.011 8 II
s1stor II
Crisonof A ?1
Total (5) 0.08
CONST. CURR. SOURCE
0.6
1
to
1
(4)
0.2
RR(4) - 100 Q
Total uncertainty (RSS) of RH(4,GaAs) RH(2,GaAs) - R.(2)
RR(2) - 100 Q
Total uncertainty (RSS) of Rn(2,GaAs) RH(4,Si) - R,(4)
RR(4) - 100 Q Total gain of null detector
Total uncertainty (RSS) of RH(4,Si)
RH(4,GaAs) - R,(4)
Feedback output /dial Total uncertainty (RSS) of RH(4,GaAs)
RH(2,GaAs) - RR(2)
RR(2) - 100 Q
Feedback output /dial
Uncertainty
GaA(4)
No.
0.2
2
Uncertainty
Ra(4) -100 Q 0.0074 5
Tota1 gain of nu11 detector 0.0075 10
Tota1 uncertainty (RSS) of Rn(4As) 0.0191
RH(2G 5) - R.(2) O.∞99 14
RR (2) -100 Q 0.0288 4
Tota1 gain of nu11 detector 0.0251 10
Tota1 uncertainty (RSS) of Rn(2GaAs) 0.0395
RH(4Si) -R. (4) 0.0158 20
RR(4) -1∞Q O.∞174 5
Tota1 gain of nu11 detector 0.0075 10
Total uncertainty (RSS) of RH(4Si) 0.0190
RH(4GaAs) -R.(} 0.0104 10
RR(4) -1∞Q 0.0022 6
Feedback output /dial 0.0050 10
Total uncertainty (RSS) of RH(4GaAs) 0.0117
RH(2GaAs) -RR(2) 0.0384 12
RR(2) 100Q O.52 6
Feedback∞tput /dial 0.0050 10
τota1 uncertainty (RSS) of RH(2As) 0.0391
N. Nagashima, S. Kawaji, J. Wakabayashi, Y. Yoshihiro, J.
Kinoshita, K. Inagaki and C. Yamanouchi
RH(4,Si-MOSFET) RH(4,GaAs/AlGaAs) RH(2,GaAs/AlGaAs)
163 046 093
Results indicate that RE is not independent of device.
material, and Landau quantum number.
A. M. M. Pruiskeh (1983)-
axx anc' °xy a r e ^dependent scaling variables.
dilute i'w»t»n-t(r»i tnpdti
N. Nagashima S. Kawaji J. Wakabayashi Y. Yoshihiro J. Kinoshita K.
Inagaki and
C. Yamanouchi A. M. M. Pruiskeh (1983)
RtI(4 Si-MOSFET) RtI{4 GaAs/AIGaAs) RtI(2 GaAs/AIGaAs)
Comparisons:
0.093 0.040 ppm
of devic~
materia1. and
dillAte htlJ
Rκ • L'X R". C.l)
T. Ando / Universal scaling relation of conductivities in quantized
Lain
Short-Range Scatterers
I • " •!• i
S1-M0S NC100) 72-17H53-33 H - 15 CT) Vsd= 0.5(mV) T » 350
(mK)
I -
0.0 0-1 0.2 0-3 0-4 Hall Conductivity (-e2/fi)
Fig. 2. Flow linrs for a t r and o t l. for the lowest two Landau
levels. The proportional to oxx and the Hall conductivity for
different energies and system Four points denoted by same marks
correspond to a, t and ax,. of a given energy system- sizes. Note
that the origin for the Hall conductivity of the N - 1 Land shifted
I / the amount — e2/k.
T. Ando / Universal scaling relarion 01 conducriviries in quanri=ed
Lan.
1.0
X Q:/ a yJx
E
0.0 0.1 0.2 0.3 0.4 0.5
Hall Condud ivity (-e2 tn ) Fig. 2. F10w lin.-:s for σ'.u and G.H
for thc lowcst twO Landau lcvels. The proporuonal toσ¥r" and thc
Ha11 conductivity for different energics and systcm Fourpoin
denotedby same marks coπespond toσ syste siz:~. Note that the
origin for the Ha11 conductivity of thc N -1 Land shifted l:.the
amount -~2/h.
5 Si.-MOS N( 100)
3
Vg CV)
@ .
p.CD It)r ~
0.6 0.8 1.0 T(K)
FIG. 2. The upper portion shows the T dependence of (dpv/dB)m" for
Landau levels N-0\, If, and 1J; the lower portion shows the T
dependence of 1/A5 for the N — 11 and 11 Landau levels. The open
symbols are data taken in a dilution refrigerator, whereas the
filled symbols are data taken in a }He system. The slope of the
straight lines gives {dpxyldB)'"" —T~' and LB~T* with K-0.42 +
0.04. The typical uncer- tainty in T k - 0 . 0 2 K at 0.4 K.
1295
0.01
q1
0.1 1 T(K)
{
0.1 0.2 0.4 0.60.81.0 2 3 4 T(K)
FIG. 2. Thc uppcr rtionshows thc T dcpcndcncc of (dp"/dB)mu for
Landau Icvcls N -01 1 t. and 11; thc lowcr portion shows thc T
dcpcndcncc of 1/6B for thc NItand 11 Landau Icvcls. Thc opcn
symbols arc data takcn in a dilution rcfrigcrator whcrcas thc
fil1cd symbols arc data takcn in a 3Hc systcm. Thc slopc of thc
straight lincs givcs (dp"/dB)"'U -T-~ and 6B-T~ with 1(
0.420.04.Thc typical unccr- lainly in T is -0.02 K al 0.4 K.
1295
SH Si-MOS N(100) 12~7H5333
8=15(T) V=O.5(mV)
T(K)
- u
•
V <
-24
a
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h a z = - a i s - - a a
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IAllllly.'/"amtlf;j72
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π/2.
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i;:oi?--'" ~_ ... ‘
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8
MAGNETO -CONDUCTIVITY σm Si -MOS N.{100 ) SN5 -16 H = 150 KOe T =
.3.3K
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Figure 6.3.2 Hagne to-transport ir» a high quality sample at a
temperature of 100 mK. FQHE Is observed at 2/3. V 3 . 5/3. 3/5.
7/5. 8/5. and k/7. Intriguing structures are also present In pxx
near U/S and 3/4 (Boebinger et.al. 19g5aY'.
2. U S.
3. 4 ft
L J
ν= pj 4í~ι fh e rfJ. r ~y r.
0.5
4 - x x
Flgure 6.3.2 Magneto-transport ln a h1gh qual1 ty sample at a
Lemperature oC !OO mK. FQ Isobserved at 213 ~'3 5'33/5 7.'58/5 and
1/7. Intr1guing structures are. a1so present' ln Pxx near '*'5and
(Boebl.nger et. 'cil. 19al.
o
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k
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A
r b t
E E E E B E E E E Z J
NeI
~...l
l =
1 -
‘F
--e
B''ATe-
A
H
R
e
F 4
>:: π? zfiω r!!
M H
r d
G
S :;;. ::s c;:)
‘' τ~
V
h
.. 4 ~
h F
ω
p ' s . 0
" 1
0.44 0.26 0.22 0.19 0.16 (0.41) (0.32) (0.23) (0.19) (0.17)
m -I I I 1 T 1
0 1 2 3 4 5 6 7 8 9 10
z ea
[P(z:z;](Z: -z;/
p" (x ~ J " ~ θ /YJ: 1) J .d. I
lij=2aahfaas/ ~=" - IC
11'j = 2 ;ft~.
N-pl.rtle {-~ (~
%(zf-z;y lo
lL...!. tJ~
e-Q2
(1)-INDEX
0.44 0.2s 0.22 0.19 0.16 10.ω) 10.32} 10.23} 10.19} (O.17)
0.51 __
*
J
W
........
J U ' s e u H F L
4 h
~
~ S ~
?
4.t lj. S
~i<'~. ν=3
CZo)=(z:-z-jVννz
J.r1Iost N+( f4ι .t; S.
(1 j) &( f). .s ieleetro N~ →//
ψcz-J=?fZ7-zfJψ
(T;tl ?
Lωd ιrite"'0
2 2
4--0 "' cddre" e F'
-') o
nv
d Ofω .t
enerl Y .d ( =fCA/s(A
t(jEt111~( 5)!rA I proj ~de rl. osc.'/ltdor s f:r~" f
faj=ds.IA~AAI protletl 5tr~ c.~(( re D.c.tor
. = f" if!c.ieJ. J.eHs ''1; "fEr~ι1
Una
I
rt ↑
ω
s d . k e N B - - N F U
~
h
" .mmr
L
F - N
$
-c .:t
e
(2 21)
N
Z. .e" t. "11 → 1tf
= pjfz.tp [P(zo ..) or; J 1i1= a
↓ ::""~ 'J 'fb..
Z'A2E11"(-)(Ntf -1
2.. 1.'.l 1-.£ 0%
IJft
"".
μ t ~t ~1J.~flI
.(11 < I t.l.-41. sl"tlfLfry
!'I
orJ.er ;N-(N-υ=fN
N4 = 3Ni= .;. /1/
•&^
^
-
(2.) p. '( I AHc.l}OMfl.t ' S~ ~'r""" P hlS' R;..;. 8 J! (1111) 3
~J~
I11¥ 1': 1/. ~t P t ps t~ 10 S p"'" a
~~~ Pseμeωωω“ddωes (t' -J;)
l π(2.; J;) ¥.tT I..J44
→:=:'1 'J rl. ~dl
6. ~ Iv. ¥.4ilel t/C Aro~4S scJ't'e 1ft~.~. .u (/ft+) J2
LA~. 711 if!. ;. þ~.B er '1 pt1IU '"
l}μμ{;J;;J H (1.) H+rV(r-(e)
J tJ~ +1. 0 1J. ~.s
dWJ s iJ.'f~.) I -J.t.o _..". dιz(ti-z.} --~ <.ψ(l.) ( 1i.
~ JJ1~' 'Z.(I) bf.ll2
“ ..
-c::'
h
11
↑
j
>- ↑
L 2 L
i! ¥..b
u
R
h u
FIG. 2. Diagonal resistivity p« and Hall resistance pxy
larged section (a) of Fig. 1] at 7 = 100 to 25 mK. Filling tors v
are indicated in pxx while quantum numbers p/q shown in pxy.
fky*.Uv.*Jt. I? CfV 177!
.7. t.1j![J
823te . .
t 3.. ...;'"
j
@ ιν 1/ 6tl. < 41Z3.
ν:::: 27f1.ltn M R
(7-w zFAf-ftMdEJ
4 6
FIG. 2. Diagonal resistivity pxx and Hall resistance Pxy largt::d
section (a) of Fig. 1] at T = 100 to 25 mK. . Filling tors v are
indicated in px~ while q.uantum numbers p/q shown in pxy
l)nJ1e.tt . e:f 01. F/1.Ys. Rev. i..JJ.. εf ('1'7/r
IU
6
MAGNETIC FIELD (teslo)
FIG. 1. Diagonal-resistivity pxx data for various tilt angles 6 at
25 mK. Arrows mark field positions of v •- f filling factor.
Resistivity minima above and below the v -> f feature occur near
v*-j and y-, respectively.
tn d.al. . M/i.lj £2
Pf
(¥vJ1F.?i ; Pγ.~. ~. ~γ. '1 - fJ }γ.J ?η:'"
pιR3 :lílf~ )
5
7‘11
a> n
7
FIG. 1. Diagonal-resistivity PT'T' data for various tilt. angles e
at 25 mK. Arrows mark field sitionsof v -t filling factor
Resistivity minima above and below the v featureoccur near v
5and.respectively.
7 6
•2
v> '
t
.•
tt
~ M
AA }
J
λ ' @ 4 k
H
M
U
↑
-v
. .
E
)
J
1
.b
is
r
i
c h
↓ h r
¥
' U
v u L G
h r
- A
.. t
5 1
l
‘
U
. U
. U
. ';;;.
Q
/.1
h
d u L a q A w h J 1 6
( h u L u h
MLEA‘
h h
f
E
4 1 " I >' ! ‘r
<&l '! aR'
tY
u
~I
lv
a h G
t. -. ut .~.
}
-.
d y s ω
R ' μ
- 'Fiv
hv
h j
X S Q
g e v
( d a E J W A
-
Jwdve
‘
p d r
. 4 m A W
JFS d w sJ u w k g h s
STSavow-
"
=13 3 ~
U 4 0
'
¥
ω l
A S S ω A O t S 1 "
-84 -
& h v o g q k a
L U F 2 u v
…
s Q
II
vhv U
d r
w d @
: +
qsgw'dA4~4v
M S b
@:
+ A
)1
+ g
4
d v
H o d - J )ω
v d
- P S
~ e "'-v-
r u
M E J
w
~e i.
ι
S e M
U 3
4A7 1T
l(←→l(
~". 1.o<LA-n.
00 <c
Errp.‘
t J
A H
u
d
(
d h
'tμ
3 1 Jm Q U o
~ ι
- A Z J
U . m g
R V T - s 1
d - h d A m
↑( C A A }
3 ( l y - G
J d N
3 S 0 5 ω u r s
d hw
¥…J
ψ - L U
4 t
( d v H (
M W S E J L ~
q F 3 “~ 3
L
I M U
- 1 0
~ t
+
mbM(}↓ A
( J S H L
a J
L
- w i
T
↑
u f
.
W H h h
a b ~ i -
J M
( + ( )
(
L 4 + ( ) + "
3 &
-AT
v
T
or
I
V-l
A h
) γ 3 ; 3 3
J d s s y
u f ( ι w h - )
5 t f
4 2 s d " N 1 J w h A S 2 2
. S
A
h T F
M - -S
e S Q U
e d e e
¥ Z E . 2 n w ? ι J
J . J d M l g te
-
5
6
A F
(
) ! "
H H (
n d "
- ) ( w f
H L E J h
“3
u b L u q - J
L
M L J
-
-11 t
t q b 4 1 q γ B 4 2 7
7 4
l p h W 1 1
1 l
F M M n d p
M H
m
O H W (
l
{ 3.
F J A P J
-93 -
3 i s l z m w h H J
- J S - e
v d d l )
( (
r i 4 2 d d
L
A
i H 3 ( ) )
t~ r ? " ι t M
U 2
d Z F - ( U d v S 3 L 1 3 a u H
-A@
~
z
4 3
] . 4 2
J h w t A U 4 4 d w M A W
4 1 λ - R h
u m T l j
; ωr 1 3 Q U H
-94 -
Q H ↑
b
G
- 95
tzz-J~Aυ
p~ι~.....\?~(.(')
[ω…?J4 i ←~.I -t'.1. Cf":- . . . 1f
l AfW 1¥. e-efj
~~.-(;'1'11
) <~/ :J~ rne~t
>t~ P.eÙ.J&2
'J ca~le.~s "L-(
cowt7"... t-IYωIf.ε.a:;I1~tÞt UI.Jt(
(;-7<.1..4'c.l1. )t.
O in
h
E
? ? 4
3 3 §
( 3
b T A W - e
i 3 4 6 1
Z U H ) '
¥ + ? " " ?
( P 4 ω
;
+ N ( 2 L a s t J
i L i F J 8 3 4 i
-96 -
Haldane
- 97 -
J~
2.. ~
3. lL
lD 5{( ~1-sØ1 loe\"'~
H=jSC5J
J)o.) =Slc:>1)[;]zlh}33 t d S 1$'7η l1~
S1;'m7 fJ"
S:: 1/2
--z
cp
h.D.
s= L '(i! b ) StIAH"! J \0.~ 5':..'J 0. P n -t ~ 11 }iiJ~f11
Lr')lJ¥ .l-:. lt.J
:'1'~He 's es b/ ~I-;J. (9 0(3)σ
~n1 ;xεq%'1.4
( )
3 F
15::
c/2 fI
N
o t u T D c
g
H
( ' o - )
(
.~
}
J
CQ
N
C A m
- q y e U N
H
f . U J
~:. 1b L-td I1 ~
{ h
+
(ω
1ω j
ε
c
σ3
a—
I -
4*
2!i(Q2 Ou)!
Cp:L→ (Hop-f)
=1TS
ι (J) ~Ql~) =-0
l
J1-:.
ω
F
g g g
b h Y 4 v - S H F A hw h
2 g ε O H
4 r W E N C h
e
F 2 4 M
e F R O -
O c
E
6
' q r T
ε J
)
o
-V
R L E
M V
n A
11
Quantized Hall Effect of Perfect Crystals in Two
Di mens i ons
! ! l i t - - i i ; 1 4
in Two Crystals Perfect of Effec t Quan t i zed Ha 11
()
107
J
H
J
t a d z d
d t
5 J E O ) k 8 3 N l
+ (
O
J
h
h
J
v
ω
U
a H J U J V - N J 1 u z
kv
~ t E L U J 4 Z a 1 6 d h F g
V F v m t =
2 ι v h z
ι
PE--d-F'‘ E d d o JTd
109-
vdω
- I N
ti •O
-111 -
- 1 1 2 -
M V U ( £ e d } e d J J ω + M M U (
4 5 4 J L ] a H f
( υ G d u d s d z t " ) Z
T
J d v d J 1 3
.υ.d
F N J U E J Z E d -
J f f u u N d H t M
4 3 d h z p
4N
.1
O
d
t (
t J .
h
d
L
h
L
-112
d
F U
.~
'
& )
8 d 1 3 4d ↑
-d J
4
F 3 o d
1 1
- 1 1 4 -
J 2 4 - v v k d b J U J
4
+
f M M !
l z n d m Z A m
.
-vv+ Z 4 z v
J 3 v
H d d v
H
--
ω ' g t ω d - e - - J
A N U 1 3 d v -
-3
M
sbha
-114 -
'
+ 3 4 8 a r u L v t Z 2 7 ψ #
J u u
υ A 1
du
w r υ 4 8 d h V N T H
h F d y -
@
r!
y
d
L e p z d
μ P
E
14dEME
z q v r t p g
i b $ 4 4 4
L
ω
d
l
d
2
L
H t H 7 d 1/
" <:/:It
ι
l ‘W 4- o tI / ‘Jl:r -" g d
.t
T z j 5 d v k w a J
w-
6
t ρ 6 - 4 J
}
@
@ a v M M
F
nuh HV A W
d v - v v x E J 7 4 L
316
6- U
A
d
A 4 h v a
ω
d
- 1 1 7 -
g h e p + F r d b t J
6γ '
iu dz ‘.
~ 7 6 4 4 4 3 L o t s -
I s t
g
; dgou=dz
‘J 4 Md a....
+
•
g ~
•
.b
ιuι
>- b~
Theory of E l e c t r o n i c D i a m a g n e t i s m
in Two~Di mens iona1 L a t t i c e s
- 1 1 9 -
Ck
j
M 4 E b
4 7 )
. 2 6 4 4 ?z
E
+ P V
P A V }
E
121-
O
4 QS ..
Si 53
F
s-tω
id
3 ↑
.
w
∞
2D UNIFORM 89-12-13
3 4 ? " ε
- 4 F V O
?
ez 4 e
+42 H
} 4 4 1
o d
i'v
i
a
I
{α)
.' ' 'c "#
H w ....
(bl
...
S»x»»*
P. W~C#OOC_ -(PiιA
T-"'.R~p. ~eJ.hYH. l - M
l
ll
0.0
4
0.5
s~'i
=υ.::t CFP .. L F Ie.. O.
"
'
s ~
~ 3Aw--
s =
d u + i U 4 u s h ) J Mv l
u .
+ b u
a L 4
5 2 4 g )
-Eft ~....Jl J ¥ ~I! 1
-~ ..-.... 1--'---' )3
"‘. -~-
( E d d +
3
).4OE h l
3 1 u t d v J P
B
---σ
~ -1"
~I~
S d h t - bm
Fig.B
ω
-''' ..-11-= i"p .. ~ " 1 I
....Ii: 1-
-a
"
SQUARE: PHI-0 0.0 K ' I " '
UJ -0.5
N
89-11-17
11
SQUARE LATTICE 89-11-17
•133 -
0.0
1-:. ...
r'"“ ::.cJú.~ (A.F)
;?d uι.>'
ωC~~
61.
6 4.
ω1-
THEORIES FIELD
x 1}'"
4 m
2 1 2
;c-
t ' p v M
i g w R S
ε-T
4 F 4υ
ιεA. "
9
. H
( - v
Ja--4
4 1 t M 4 4
…
44u
;
.h"
j
j
J
... .i. 11
S H W
2 4
‘
f - f a i r j 1 P
A F + -
4 } -+
4 v
£ r J F
ψ
.“ G
..J
i y
‘ 3
J
+ I-L
.3
d u -h
M A P S
H
‘--.J
JwaR
3 4 6 H . A M
*1
t
2
( H .
' . . ‘ @ 1
-u'
o d M h
.‘‘ ...... EE - - e
aa-----------ili--
a b
r.J
Q
dm.
u
JUe
U ..t.
~t
li ~l
d d " J F 4 + J R ( : h y v
EF
JI~ ft)
.1$
- 1 d H S
t
O
1. h 2
( a L ? t L ι
)
d a { λ
3-J
141-
] +
a-Tg
4 4Q t N %
e M q u
}.Z
U J
3
U ν J:.R
J!
. ~- Z3
3. :J.‘ ~tfo' ¥.J.J. Hl. A-D ll\f.....f~.
i. sJ)
^ I~ td
4 6 ‘
{ d v S A V t
A V ? H J? q z t
(
<d al s U4:b 'L lZ 6
... ~ <.d "‘
<<d
J N ~
m d o
4
4
5
t1
G M O +
-
2 +
4
1
‘Leys-
λ-
4 m
U a
(w
-1-
>1
zs e k e g h
ξ
7" r
F 5 5 3 Z ↑
S
S S E - v t A F ?
(Luu
~ F -f.!: τ
U 1
l~ i ..41:1
'
O A T
M U h e
: h - φ ? n o ~ ? A H
A
hdφ 4 d
h v g ?
@v
d
l h
uz
(
‘
4 1 4
- N V
~IL
3jA
-su
d
• - P Z
1
=
....‘ s ~ ¥
..i < Ir¥~
k
rll
z q g m L S J U
§
C(~ s <::oft 1 _ ~
~~
P-
t
3 L J d A
a
£ j
‘ct.l.
jidft)3 CK
.ysu
J..
E
. r
IJ
w o e - " "
d t o v
a r A 8 4
3 v l U 3
~'" 't ~tt~ ...
* 'YO" 1-: 3
Impose boundory condition
H=8ttq→=EClk Eli nb TopoloiCQI Sohton-ωJlin0"model1
Hail-tanicu H=J{z
‘"'Qbles
ChQn3t =1.2nClln‘=l
0.0. J l+
ωe lne ‘
1T~(S -=2
of -ti.sωiMl'
"'eio" ~ Esp~(j f& II~ = int...
I.. totc.ii" (~r -E...c ~i~ nba 1;;' - E...cεsa n zzjzpo
0(("'=0
palo~i C:QI
c.lo..-:1) ~(.S
t-Uyfr •terra
' sfin less
i(S=z.s→ sa
r"~=1 ith =(::)
n.t-in~ '= ~i Cl (~}lft ~in~J. nn W" ;¥...- "lito
0( (TJ~211'. O((OI=O
spi.. leu = @8~
iot" ...r ↓ ~~A_-ω Sol 4tA.μ
=iiZf.."" )..:s1.
-.. H=l ~.
i
"&~"lσ..~
." *
H=j“
"'''''1 by
¥t
Look W a bjo energy effective* theoiy
CP model with Hopf term II ne^lcd: higher deriottt^e
model uritln Chern-S««nons t e i w
Estimate
Conjectrc (by. Wi»jman, DfaUthinckii.
Anti-{ferromagnetic system can be by the CP1 model with C~S term
setting
Result Bose-Fermi tran,ymtrtatio« ?- quanta + C - S
Transition amplitude
— 2: e
•Partition -function
z = • ^ " IB)
Estill'ltlt~ <ω..kPO~Icω
<w)=l-tiu41(+r fw.dx14l+.. > !ωεnetgy e'ectiυea kiDr
{ ( ird <A 'i'-) )I ldi! J dA~ IA..(~ e "/
/ 'cr"..cI.riIJ'~
tJ=1t:{ N.'.cf =-L A- I ¥hlh':.tA;rI¥''i' "SM It"11 ~J dA.. e '.-.
-----. -------1 :r-o
-L.!.. r(EIA.a"r~p J'P I sYt'.. ~:rrl' ... h~ø
p['fdX 14d'e
Hopt t.erm hi:¥tel" detiu-o*i&)e
1ft"
....--ftw'n
b)' iII~ CP'el c-S t"rm S'e'2P=1t
oc.lIhiftlkii. P.i)‘h J
frf
'y"-¥icJ
l1tì. ~.va"J~(w> ~DI'ItTO.W r1"te
/ StokE-s' /; zF ¥ 'lcl~M= Jd'ct.-.II E~t' i" 8 p
=Plltidllfllctll! i mie."
= '11tiiFmE151
So
-mL(f...) J _ q....“¥ q.(3t.X') = 1: e ... =.: e J
<&11')
Trick
£«i««n brocket
This \$ Bose - Fermi
Xnclu.de charged 4ermion
S
L '~C<s)dr -...2 . ^ i IPJ~ ~ds =j?dL- Id@e ""_1) ~'It' J
momt'"Frene-t-S .. .-t lQ
E' i p.o=" L =17dLPL
In -=: C Ib -e E'
C: r.siot':
ez35 8:ωNXttute
{ ctf.ij'" -'" J l = \~-dl e P21U JclC C
pto pcaIQ~o" .0 Diroc -m-iF6 u::q
":'C;
ie-IJ=tI'Ionic(-~ tit"lcC Sosonic
.• (J 1:mto:t-ion.80se -f"" $ lhit = elCp 1IdS (! clu l - ∞ l
"chA"8e-d nc:lu.delt
T...c
ot.ftra li. SU(2) {e‘~ e-b¥ = fAfe-c ....
-TrM“l Jd. e ìJ~cIS C<s d. e"o
CIS \..'~J dC r-I) ~...(s.J …~.... ($..1
Corspond...c.
= 0;. .… 0"....
Homllton (bnnalism)
Cononica! Momentum
Poisson Bracket
Canonical Hamil-tonian
Hc:= ~fFt J~ TT"-L i;.¥.'2
=gpJd~{65tz-J
zEJ}LPLeaAWJ)-zdhodFJ
θicl~ ìi dtlij 1" At<l'i'&(i-~QI E e~"ωa. Apu" }
H ittonian
ft'iaory@"ctUonE¥er-La'¥"Q1
z8εuQlrrAp+gzzepsdJ+zeahz-PJ4atzo;
φZ
L→ cletermine U;
={ Hpl~O 7 (pG'-1Ja1'(1-<i'JÐ~iJIl
ωn
Cor icolMomtwrt paE EL .-M = iq:-mQqCl'+ e~iJ
---t p.;mQl)' (on"0.;
.POisson
Then x (c'jstiuf, (wj
H T = - = isr« (If-
bro.Q:ets
x()Stl{hadBt311
n betω1¥$of¥btclckcts
{Alctl. 1T.lCjJ}D = ~ 3ij ~û-1J
{AH'.li }o=::{I¥oIII 'Tfi<jlT = 0
{(XIlfoti'J)D: dCr.'Ilo ~tl
{t p1 }o=J1J hr"u1D=eolo4"&(i'_
~8a!rc!91(fJ l H m D l
~~ !u.H:'.pliQr
H iltn;ant.otG1 ftf-tauIP-;.¥"1 -;1ð~1ι
/' noi" itdt'f'.
o
u6c~-iJ
+0... firt c.¥fAS.
?z=eεr.t Ii; ct i'I(ï~J::::1f ωhere zd"~1 =CÞ~z (i
I'wd\u~{4>t..¥ ( c'"1)st(~.Wll) J
Cst(W.~ =tqt'tWÎdl ::. -ZD fst 'Cw‘a)
( C-t~t(ùS..=t&w"J
•fixing
0
I I
{Cononi .1Qtitation> z= jldJAil~εIU?Aad e!Að<r- í(!t
iAfctJ
Eqwa"1m.ωm.ttotor X fi{l [q~~i..{}(pt'LeAAì()]
}→ TKL eJd ~i.ÅIAJ}
Gusefixins rmined o.s
=29
FO.. l. 1 -
o
/0
-to elimintit*
(-cl~-tAi.f.qQJ)(-iaal _ e-A'(({ =E"'~
hettl
a~= -;;-;dq
"<<tioft
ALl l\A)= ð~@)
(onsidet- ~li..inOlt.
AI(~I by"1tt.. tM..e 0'1 Y'.
b)' 'ThiS is o.chi91X'c:(
-ex
Ex-qQJZ tGn.QQ)=
= a~ {l:. _eo.e't'I: eCe~ .llt'J} -':s.GlCs I(~.s" &. "
..QCi
NteC dcfi)Jc.
Then
N. lot $
y s t M
show b«co«ie
({1)::: ocp[zSE}}
Sthrodnaer t
Exc.hGnSt' p ionof .-rtid •• t ~. N
:;JX::::: :l s ~ N
h... 3iωf' ~ ... ctI E...)~.
ω. shd
3 - H
V
" ( J 7 t
geET-- ζ ι
s E i g
he z a z g + ? ? v - z Q m u 2dw-aMm
2 4 t s
Ler-Tam--g ‘ i T p v a w W
q ' p w J V M q
p w d
pre
zsavHF
{ F
W M q s p Z M +
uvZ J
e
-rw - g + S d w d s r Z M "
f t
52re q s C H T (s -dm
M
In (2-U)-dim. j highly non-trtaial
quantum 3?el<i theories appear.
origin: Q\em - Simons "term
-term )
e i s -
be
Sccanonical Strycture Q~I.... "' Field ...ìe-~Chetn -SimOf¥f
b.
j: AnJul '"0"'.
eiS = e2.1t‘
Clppeo.r. 1:E'rm Chern -SilllonS
Maω" klnetic Te-rm (l.-"d. clee)
1:L _0 J=O o<<R .1 - T
Fo .. • HQ1er't hem-S¥PIIfUle"2. l - m |
~ \ii3~ -T" Mat'r
StructtAr~ is di*"rent.
δK.$'-S
Chaae oan
Constraint
There remains nw-W! <wi»%Hwv>
CLboU't" ¥ni1"mc:rtioft•
J:=-μεi~ Å~ (~T+~ )J'; -+~Wf.
USin~ M~er
~~ (Shoul~ Conatf'Ginl
e'.Il.et m
(~I- ìeAt) → e ‘ i Cð'+ !~)rp
Ehmi". ::(11.-MI
lμt3iφ= 4
l - m m l
G.I..ie. tliE. ð'=eA~ =(d;(lnli-j1atconlt.) Jd''''
←j(JnltjrCIN't.)rci)
ψωctI......... (rpa t:…..?
"
- ) commutator
: <fw> 9t3) ± e iKfty< ?tx> = •••
can show
by YSin CjrJ.me'"
CherJ¥-SinS
ω..
l
CQn ωe rer
;1._~ j(i)φ-i...1l-JJ1"." e -....-.-<pctJ e--• =-e 1' ↓
etES{.Q(i-J'}-ll'1b= "Ir I
a '"fI'r :
e hhdaE9494=
i-r -L_ .. 2~ m
Quantum Field
t ic Ma$nw>
A-B Effect
Dislocation of Crystal
¥. HrdSLl)Gl
@(-Rlff -822 (sephson1"on Incomrn surot.eCDW
(l+l)-dlm.
Chira.1 Anomal>
Optlco.l Fi ber 8e~ ~~ωe lHolonomy) tl+l>-dim.
ct- c-Rlf.P-03( HcdlE fArQ~ Rcrtation
ro';cNonon
c-t1~1e...
(-sωeU t1..1t~
aHt
M
ep‘HM }
n‘4
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3 b 3
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ν N
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ν
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l
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7
a S A B - - a E E - 5 4 E S ‘ E Z E E A q a z a z - - - 2 E E E E E
E e ' z
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ZSEs-a
se--21E E-RE32 M g f f - z a z ' 5 5 6 F E a E E -
- a z - - h t I ' S E E s - E s - S E a - b E E - a Z e - E E E E -
t M t E S a s
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E S E g - E - E S E E S Z E h e '
E 3 s S E E S - ' s t 4 E E E a S F F E Z E E 2 2
t
r
-2
- Z z a - a a - - = s a E - s E f
a h E
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e Z u - - E E
S'BEE-ssEzt2BE-ER'-SEase--sag-@-BE--gEE
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-
ah4''EnME-E-EEESE--Bez---fu
E Z E ‘ . a a ' E E
a s t - - - ‘ a a - e Z E B - - h g E E ' E ' g g p a a a F d τ S E
z s ‘ =
g e - - E E . ' e s - - E S E - t g J h z f a 4 2 s a a - - a - a s
a -
- z a - - 2 s s r = - z : z a u E E ω 4 - Z "E E ι E S Z O B . g
e
- e E ? - o a 2 2 E - B E E - Z E = E t E 5 E U S E - - E 5 2 a
z
-a E E E E B - - S M 2 s a s s
3 4 - E
E E S E 2 E g g I E E 2 E E t ‘
a E E - - E E E Z 4 E a E P
a 6 2 2 a i E E Z E E ' f h S E a s -
t s a - d z a aso. : t a z E E S T a s ' Z E E - E a E - E
hEESza--abM ' z E e S E E - = - ' Z E b a u E E - - E F
S
ERaua4F-B‘S
azs'EEEE'UaatE5'PEEPMe
a s - - B s s E E - - E = E M a e E E E Z E z . ‘ 2 E E S - F
hEE -a.ESE-Qa--EEUH
h : R ' E S Z S 4 z a S ‘ - a - z i Z a E Z“
E E E A . E 3
etasaE‘aza .. E - S E a t s - ' z a - E E a E G - -
B ‘ a s
a s a . ‘ E a g a - 1 4 : z e a E - E 5 2 3 a f
s E B E E - s i t s - a h - z s t u t - - = Z E E - E ' S
B--Mmau--=a2bahe
-oa.MadBba
a-a'zEb - B E E - E R S J h E E E S E E T E e - - - a a ea2
6E'zzS E E E ' E u a E E E B ' s t - E E d m g z
'2.'Esd-m--sa-2aZ3vs-aa'a"EzeAL2 H
e E - E a J a a
E S E Z E s a g a - - z q a u - - 3 . a 5
4 s t g - a E a a z o - - U E S t a - - a S E E M E TEEgd ZX
'a- n d
h a A E E S h
M 4 3 2 £
-e-EB--
E
; j i - - t
~
E ~
e M
ω .
¥
ι
50 60
Fig. 3. Low-temperature resistivity of a sample with .v(Ba) —0.75,
recorded for different current densities
s.
-a a
ldaLLH ~1I 11.
? H
4~~ ..ft
1:~~n.f
fo= h.cl'Ie
30 40 T (KI
Fig.3. Low-temperdturc rcsistivity of a s>llTIplc with x(Ba) ~
o. 75
E ordedfor di!ferent currcnt dcnsitics
7.5A/cm2
2.5Alcm2
0.5A/cm2
2 -
SOUIO magnetometer Toroidal solenoid \
40 60 80 100
E
--
z
50
TEMPERA TURE IKI
FIG. 2. 1-V characteristics of Nb/Ba-Y-Cu-0 point-contacl junction
with the application of 8-GHz microwave radiation. Voltage steps
can be clearly seen.
. fa.
n t
I l l 1 1 M I l l i l i - - l i l -
-l111111114
llluJ1
'" -;t./J
a O O N '
fIG. 2. l-V characteristics of Nb/Ba-Y -Cu-O Doint~contacl junction
with the application of ~GHz microwave radiation. Voltage steps can
be clearly seen.
40μV O 40Jl'V
-174 -
E
E
~
(BiO)Sr CaCuO. (TlO)BaCaCuO.
(b)
-175-
(a)
- J D
r z
M «_
0.1
$ This work
- 1 7 7 -
1 1 1 1 1 1
l l h i l l - - f l i l i - - -
E
E
Shafer.et al.
!18
^ 1 !
. dln7c/dP t 7CJ • ; Nd,.,,Cteo.iiCuO,-,(NCCO), O :
Nd,..Ce0.,Sr..!Cu01.i(NCSCO), • , + , J7 ; i Y - « J:
[/Eu-Ba-Cu(M)-O(M=Fe, ;
i I
! I I
P I * . A. ; Y-«i'yGid-B;a-Cu-O, ,D,: * ; Bi-Sr-« i U
TI-BarCa-Cu-O, ^A, X ; La-Sr-Cu-O(lSCO)
(QPd) 7;
\ I V
X (Ce) X (Sr)
1! I M - - - -
C 1 M /
I l l 1 I l l i - - - hIli--v l i l - - A M I l a s - -
- d p ¥
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l i - - J -
-
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l
i
m
i
H a F Z ¥ E
40
Tc(K)
d In Tc/dP
φ: Nd...Ce""CuO._(NCCO) 0: Nd.Cesr...CuO._(NCSCO). .+ v;iY-E
Eu-BaCu(M)O(M=Fe.
pO.~i.t(' Z 0; Y~Ba-CuO.
i:~:vd P-CO.
:d.. X ; La-SrCu-O(LSCO)
A U V H
z ‘
d -‘
10-1i 0 ~ :z:1
• RH>O
N h J P h h / ¥ b N
b¥l N V "
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««« T-J MODEL THERMAL CYCLE DATA PLOTTER »«* INPUT FILE NAME ».DAT;
»«Q42O1T
V .03 eV
SIZE SPEC,; <12*12»12> HOLE SPEC; D • .0700 HOPPING SPEC; TO
» .30 HOPPING SPEC.; Tl . coupllnc J • • 1 eV * of STEPS (ONE WAY)
- 40, (INITIAL Beta) • 200.0 1/eV (d«lt*BBTA) • S 1/eV. WARM UP
SWEEPS • 0; RET to continue
AVERAGING SWEEPS • 400
J = 0.10000 [eV]
Abscissa 50 [1/eV]
J - 0.10000 teV]
i—_—i—
T1 .
317
0.00050 [eVl 50 [J/eV]
- τJMODEL TKERMAL C~CLE DATA PLOTτER ••• INPUT FILR NANE ..DAT:
..0420IT
S1ZISPBC.: <121212> KOLI SP!C.: D .0700 HOPPINO SPBC.:
TO.30eV HOPPINO SPBC.; TI.03eY coupllnc J.1 eV
• 01 STBPS (ONB WAYl40. IINITIAL Bt2200.0l/eV (d1ta8BTAl l/eY. WAR
UPSWBBPS 0: AYERAGING SWEEPS • RET 10 con 11 nue
417 2/17
1 scale= Ordinate Abscis9d
Phase 1 scale= 50 [1/eV]
PHS4201T.DAT SIZE SPEC; <MM1»MM2*MM3> where MM1*MH2*MM3 <
12«»3 MH1 > 12 KM2 - 12 MM3 > 12
Tl » .030000 D • .070000 Be « 400.0
/ / / / r — \ —— r —• r —- T —- r —— / / / / / / / / / / /
N - . N N N N N N N V N S / / / / / / / / / / /
-— J •—• J •— J •— 1 -— 1 -— J / / / / / / / / / / /
/ / / / / / / / / / / 1" •—• I — I —- I — I —• T —- / / / / / / / /
/ / /
S N N S S S . V N N N S N / / / / / / / / / / /
—' 1 — 1 — 1 •— I — 1 •— 1
1 —' i -— 1. —— V -— 1 -— 1
SHEET 1
ROTATION ANGLE
THETA = 0.
77=.o3 t>- 07
'ft'here MM1+MM2101M3( 123 PHS4201T .DAT SIZE SPECo
(1011011101M2101M3> 1041011 12 ""2 12 101M3. 12
l'
. .~:.~~~..""
¥
/
¥
‘.
' ' r ' r ' F J F J J ' J ' F J P ' r ' J '
J
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¥
J ' r ' r ' ' ' ' F J J ' J ' ' ' ' p ' r ' r ' ' ' '
le/!.
Phaee
- . I
1
1
SHEET 1
ROTATION ANGLE
I t t I I I ! I I I I I
1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
1 I 1 1 1 ! ! 1 1 I I I • / • \ « / » \ « / « \ " / » \ » / « \ « /
« I I I / 1 I 1 1 1 I I I
1 1 1 1 1 1 1 1 1 1 1 1 • \ ' . / . \ . / . \ . / . \ . / . \ . / .
\ .
1 I 1 1 l_l 1 1_1 1 1 1
° 1 1 I I I I 1 1 1 1 1
I t 1 1 I I I 1 t t t I
1 1 1 1 1 1 1 I I I 1 1 • \ . / . \ . / . \ . / « \ . / . \ . / . \
. 1 1 1 1 1 1_1 1 1 1_1 1
THETA = 0.600
o shows + dev.
Max. dE = 0.01041 [eV]
ROTATION ANGLE
THETA = 0.
PH54201T.DAT SIZE SPEC; <HM1*MH2*HM3> whare MM1*MN2*MM3 <
12**3 MN1 • 12 KM2 - 12 MH3 • 12
VI D Be
.070000 400.0
PHS4201T.DAT SIZE SPEC; <MH1*MM2*MM3> where MM1*MM2*HM3 <
12**3 MH1 • 12 HN2 • 12 MM3 • 12
Tl - .030000 D • .070000 Be - 400.0
SHEET 1
Max. dE = O.141 [eV)
'i E. a o ' 1 l -sAO'l i EE--BE. l
J
-
/
-
¥
↓
/
-
¥
-
¥
l o - -
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l o l - - 1 l o l - - a l - - l l 1
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where 1H23< 123 PHU201T.DAT SIZlI SPl!Co <1111123) 11111 12
11112 12 113 12
whr 111111111211113< 12..3 PHS4201T.DAT SIZlI SPl!Co
<l1111211113) IIM1 12 z~ 12 11M3 12
N H h l
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**» T-J MODEL THERMAL CYCLE DATA PLOTTER •** INPUT FILE NAME *.DAT;
*'G4808T
SIZE SPEC.; <12»12*12> HOLE SPEC; D • .0200 HOPPING SPEC; TO
• .30 eV HOPPING SPEC; Tl » .03 eV coupllnf J > .1 eV
» of STEPS (ONE WAY) • 60, (INITIAL B«t«) > 100.0 t/eV
(daltaBBTA) • 5 1/eV. WARN UP SWEEPS - 0; AVERAGING SWEEPS • 400
RET to continue
J = 0.10000 [eV]
en I
Radial part
317
[eV]
l
ι W A F
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nu
a n l
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• • • • • • •
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- T-J MODEL THERMIIL CYCLB DIITII PLOTTER ••• INPUT FILH NIIME
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400
SIZH SPBC; (121212> HOLH SPBC.; D. .0200 HOPPING SPBC.: TO.30eV
HOPPIGSPEC.; Tl .03eV coupllnl J.1eV
6fSTEPS (ONE WAYl60 !1NlTIIIL Blal100.01/eV (d11BHTIIl 1/eV. WAR
UPSWEBPS. 0; AVERIIOING SWEBPS RET 10 Qon tI nue
'4
[eV]
J
-'.-....-'.-......' . .' .I
← - -.h ..............-..
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CORELATIONO 1-5 '••<*•:
CORELATIONO 1-79 CORELATION 1-79
aM
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1e/1?
[1/eV]
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• • . . a
R
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Rediel part
A 6
I I / / / - / . - - / / I / — — - - S \ \ I \ \ N —
\ \ / • " / - - v \ - \ \ \ 1
S \ 1
l / / / / s \ *• \ y \
\ I i s
bond length = 2Eave
Max. dE = 0.03509 [eV]
PH5487tT.DAT SIZE SPEC; <MM1*MM2*NN3> where MM1*MM2*MM3 <
12**3 NN1 • 12 NH2 • 12 MN3 • 12
Tl ' .030000 D • .020000 Be > 400.0
One of typical non'periodic CONF1QURAYIONS teen among 12
sheets
FHS4B76T.DAT SIZE SPEC; <MM1*MH2*MM3> where MM1*MM2*NM3 <
12**3 MM1 > 12 HM2 • 12 MM3 • 12
Tl • .030000 D • .020000 Se ' 400.0
SHEET 4
bond Jength = 2Eave red circJe; Max.dev.
Mtx. dE = O.359[eV]
h
l
i
PHS4876T.DAT SIZE SPI!C; <MMlMM2MM3> MMl 12 2 12 M3 12
wh.re MMlMM2MM3< 123 PHUI78T.DAT SIZI SPI!C; <MMlMM2MM3>
MMI 12 11M212 2 12
l N H
n u n u
n u A U
A u n u
- E - a
One of tYPlc1non-perlodlc CONFJOURAJ!ONS .een a..onl 12heet
SHEET 4
red circle; Max. dev.
Max. dE = 0.03509 [eV]
oo PHS4t7tT.DAT I SIZE SMC; <HH1*HH2*MN3> where MN1*MM2*MM3
< 12«*3
NN1 • 12 HH2 • 12 NH3 • 12
Tl • .030000 D • .020000 B« • 400.0
• •• T-J MODEL THERMAL CYCLE DATA PLOTTER **• INPUT FILE NAME
*.DAT; »«G4807T
SIZE SPEC,; <12»12»12> HOLE SPEC; D > .0050 HOPPINO SPEC;
TO - .30 eV HOPPIJW SPEC; Tl " .03 eV couplim J - .1 iV
* Of STEPS (ONE WAY) • 60, CNITIAL Bit*) • 100.0 1/eV (del((BETA) •
5 1/eV. WARM UP SWBEPS • 0; AVERAGING SWEEPS RET to continue
J • 0.10000 [eV]
SHEET 4
JO.10000
1 8CIII e~ Ordinote Absci 8811
- T-J MODEL THERMAL CYCLE PATA PLOTTER ••• INPUT FILE NAME ..PAT;
04807T
400
91ZE 9PEC.; <12u12> HOLE SPBC.; D. .0050 HOPPINO 9PEC.; TO'
.30 eV HOPPI~O 9PEC.; T1.03 eV coupllnl JJ .V
• Of 9TEPS (ONE VAYl60. ('NITIAL Bt3100.0l/eV (dl1aBETAl l/eV. WARN
UP 9WEEP9 0; AVERAGJNG 9WEEPS RET 10 con tI nUe
-- -.-.. -.. . . . . . . . . . . . .
. . . . . . . . . . . . . . -. . . .
nv
u
‘h u b p
PH547T.DAT IIZI I'IC; <NNlNN2NN3) E 12 NN2 12 3 12
l M ∞ l
J = 0.10000 [eV]
CORELATION0 1-3 CORELATION 1-3
I Order Parameter 1 •.- A^i"".' Order Parameter 3../ i> '
•;/••'. • Radial part
C0RELATI0N0 1-5 CORELATION 1-5
{
-
'
.• -F
- q
(lIeV] Phoee
/ 1 J
SHEET 1
bond length • 2Eave
Max. dE = 0.05202 [eV]
PHS4t6ST.DAT SIZS SPEC; <NN1*MN2*NH3> where MM1*MM2*MH3 <
12**3 MM • 12 NN2 • 12 NM3 • 12
Tl ' .030000 D • .005000 Bt • 400.0
No periodic CONFIGURATIONS seen iioni 12 iheett
PHS4SStT.DAT SIZE SPEC; <MM1*MM2*HM3> where MM1*HM2*MM3 <
12**3 NM1 • 12 NM2 • 12 HM3 • 12
Tl • .030000 D « .006000 Be « 400.0
.."~~.. "a
SHEET 1
Max.dE = 0.05202 [eVj
where MM1MII211113< 122 PHI4S6eT. DAT SIZ! SPEC;
<11111MM2MM3)1 12 2 12 H2 12
PHS48er.DAT SIZE SPEC: <MM1M211113) where IIM1M23 < J22
1IM112 212 M3 12
I N N - -
B 400.0
o o
o o
o o
o O
INPUT flLE NAME ... DAT;=G4402T
SIZE SPEC.; <12121> .ESP o= .0700 lPPINGSPEC. ; TO = c 30 .V
'PINGSPEC.; TI .00 .V couplJnl J:= .1 eV a 01 STEl'S {QNE WAVl 60.
(INITlAL Bta) 100. 0 1/.V (d1t.BETA> = 5 I/.V. WfulM )JP SWEEPS
= 0; I¥VERAGING 5WEE'S = 400 RET t"o contlnUIt
SI1EET 1
J = 0.1αm
PHS4866T.DAT
"" "" -
n u p s -
1 M M M l
(2. X/2.fβ= 1(1:l"';400 D: .07 Tt= 0 (; /2/CI P=I∞H 00ρ&!' .
CI7 il=o.
S17
\
\
\
S
s
N
PHS4406T.DAT SIZE SPEC; <NH1*HH2*HM3> where HM1 ' 12 NN2 >
12 MM3 • 12
Tl ' .000000 D ' .070000 Be * 400.0
1 /
Max. dE = 0.00700 [eV]
PHS440ST.DAT SIZE SPEC; <HM1*NM2*NM3> where MM1*MM2*MM3 <
12**3 MN1 • 12 MM2 • 12 HM3 • 12
Tl » .000000 D > .070000 Be " 400.0
SHEET 2
where NNlNN2.NN3 < 123
PHSHOT.D.¥T SIZ! SPEC; <NN1.NN2NN3> Nl 12 NN2 12 NN3 12
..here NNI.N2.NN3 < 123
PHS“06T .I).¥T SIZ! SPEC; (NNl.HHZHH3 NHl 12 MM2 12 MM3 12
l N N U l
n u n u
n u n u
n u n u -
n u " ' n u
.•
n u n u
n u n u
n u n u -
--a-
I to bo
Max. dE = 0.00700 [eV]
FHS440ST.DAT SIZI SPEC; <HH1*HM2*MH3> where MN1*NK2*MN3 <
12**3 MM1 • 12 NM2 • 12 NIK • 12
Tl • .OOOOOO D - .070000 Be • 4 0 0 . 0
• * • T-J MODEL THERMAL CYCLE DATA PLOTTER • * » INPUT FILE NAME
».DAT; *=G4605T
SIZE SPEC.l <12*12* 1> HOLE 'SPEC. ; D = . 0200 HOPPING SPEC,
i TO = . 30 >V HOPPING SPEC, i Tl - . 00 oV
coupling J » . 1 iV tl of STEPS (ONE WAV) » E0. (INITIAL Btt«> -
100. 0 1/<V <d>lt«BETA> - E l / .V. WARM UP SWEEPS = 0;
AVERAGING SWEEPS • RET to continue
t'"..
l M N h l
PH1440dT. DIIT SJU SPIIC; <MMlM2.MM3> where 14141MN2MN3 <
12..3 1 12
""2 12 z 12
Tl.000000 D • .07000
Max.dE = 0.00700 [eV]
INPUT FILE NAMl! ...1;46051
SIZE SPEJ::.: <1212 1> IJ:.E'SPEJ:: D" .0200 ll'I'l.SP '.τo~
.30.V HOf~ING SPEX Tlz .00 eV euplln.J = . I .V
• .1 51PS (()f WAY)" 60. C¥NITIAl. B¥0)- 100.0 1.v (d.1 taBETA>
. 6 I.V. WIII¥PS:EFS=:1 0; 1¥'INGSD'S40 RET to eont1nu
• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •
• • • • • • • • • • • .J‘ •
- E
J.5
XM8OOU
J = Dl(
.".)..~~-)# Pse
i
N
l . . '. . ".
~.JI' _'~.‘._..t .. ..'
1 le= 50 [1/eV)
. . n
':.:'
IZXU.;(
Phase
β. (00 'v0::> .0) 1=0 12λ//β100-4.00::. .02 Is: 0
- \ I I I / I \ - \ ~ ^ I i s - \ \ ;
s I — / ' s s I *~ / s s -- S \ \ \ - \ 1 \ _ _ / • / — / ^ •" -- N
\ I / /
\ I \ — - - / N ^ \ \ \ —
SHEET 4
ROTATION ANGLE
THETA = 0.
••« T-J MODEL THERMAL CYCLE DATA PLOTTER •»• INPUT FILE NAME *.DAT;
*-G4302T
SIZE SPEC! <12*12* 1> HOLE SPEC.; D > .0060 HOPPING SPEC;
TO • .30 eV HOPPING SPEC; Tl « .00 eV coupling i * .1 eV
• of STEPS (ONE HAY) • GO, (INITIAL Bet*) • 100.0 1/eV (ddttBETA)
> 5 1/eV. WARN UP SWEEPS • 0; AVERAO1NQ SWEEPS RET to
continue
PHS4B05T.DAT SIZE SPEC; <MM1*MK2*MM3> where MM1»MM2(MM3 <
12**3 NM1 • 12 HM2 • 12 MM3 ' 12
Tl • .000000 D • .020000 Be ' 400.0
Typical non periodic configuration aaonx 12 iheeti.
J • 0.10000 [eV]
SHEET 4
- T-J NOOEL THERNAL CYCLE DATA PLOTTER ••• INPUT FILE NANE
..OAT;.04302T
9IZB SPEC; (12121> HOLB 9PEC.; D. .0050 HOPPINO SPEC.; TO.30.V
HOPPINO SPEC.; TI .‘00 .V couplln J. .I.V of STEPS (ONE
WAYI60
(INITIAL Bet} 100.0I/eV (d1taBETAI I/eV. WAR UP9WEEPS 0; AVERAOINO
SWEEPS • fl:n to CDn t 1 nue
…G …
J
i
J
J
400
"'here MMlNNhM3< 1243PHS480OT.0I.T lZI!SPI!C; <NINNZNM3)
l1li1 12 IIItZ 12 NN3 12
l M M m l
O. 10000 [elJ] 50 [l/eV]
1 8cele Ordinete Absciese
Typlcal non perlodlc conflurIlonaona;12heeta.
'•"!••' ?T .t.....|tl,r....i1..:.i J - 0.10000 feV]
] scale= Ordinate D.00050 [eV] Abscisea 50 [1/eV]
CORELATIONO 1-3 CORELATION 1-3
•
Order Parameter 3. H.."*i5*-V<""~" Phase 1 seale= 50
[1/eV]
CORELATIONO 1-5 ...*pi''*r:?' CORELATION 1-5
Radial part : '•'• • ? • • • ;—i .<- ! • : .
"77=0 £>».o»«r
Radial part
.. 1 ~J<!τ
•*. ~ ** s 1 ! \ ^ / • ,- \
I y — \ i / / / / i - - /
SHEET 2
ROTATION ANGLE
THETA = 0.
*•* T-J MODEL THERMAL CYCLE DATA PLOTTER »*» INPUT FILE NAME «.DAT;
»«Q42O7T
SIZE SPEC,; <12»12«12> HOLE SPEC; D • .0700 HOPPINO SPEC; TO
« .30 eV HOPPINO SPEC; Tl « .06 eV coupling J • ,1 eV
* of STEPS (ONE WAY) • 40, (INITIAL Beta) ' 200.0 1/eV (delUBETA) -
6 1/eV. WARM UP SWEEPS > 0; AVERAGING SWEEPS s 400 RET to
continue
PHS4305T.DAT SIZE SPEC; <MM1*MM2*MM3> where NM1*MN2*MM3 <
12**3 NM1 • 12 NM2 • 12 MM3 • 12
Tl • .000000 D • .005000 Be ' 400.0
Typical non-periodic confifuratlon aaong 12 •heeU. None of then are
commor in flhape each other.
J • 0.10000 [eV]
1 scale* Ord'nate 0.00500 [eV] Abscissa 50 [1/eV]
- T-J MODEL THERMAL CYCLE DATA PLOTTER ••• INPUT FILE NAME
..DAT;24207T
SHEET 2
SIZE SPEC; <121212) HOLE SPEC.: D. .0700 HOPPING SPEC.; TO. .30
eV HOPPING SPEC.: Tl. .06 eV coupllna J. .1 eV
fSTBPS (ONE WAY)40 lNlTlALBel3200.0l/eV (dellaBBTA) l/eV. WARM UP
5WEEPS. 0; AVERAGING SWEEP5 • RBT lo contlnue
ROTAT ION ANGLE
400
fHS4306T.DAT
SIZ! SP!C: <MMlH2MM3) vhere MMI.MM2.MM3 < 122 1 12 MM2 12 MM3
12
1 M M ∞ l
1 6cele .. Ordinete AbscisSd
n W E n - -
--aa
••• 1
R U S E
TyplcInonprlodlcconflaurallon aona12 heel.None of lhe.recommor 1 n
ahpeechother.
J = 0.10000 [eVJ
CORELATIONO 1-3 CORELATION 1-3
Order Parameter 1 ,?«:'•"•'
0= .0*7
Order Parameter 3
CORELATIONO 1-5 CORELATION 1-5
-.
1 scale= Ordi nate 0.00050 [eVJ Absci ssa 50 [l/eV)
F
. .
CORELA Tl ON 1-5
7f s . 06 {):: . c) 'i (30;1-00 -1'00 12"'1 ~/2.
I 1 \ \ 1 I I \ I I I I
! I I I t 1 1 1 ! I I I
1
0
o
0
o
o
o
o
' 0
o
0
o
o
o
O
0
o
O
0
O
o
0
o
0
o
0
o
O
o
o
O
0
o
o
o
o
0
O
O
o
o
0
o
o
0
0
0
o
O
o
O
o
o
0
o
o
o
o
o
o
o
THETA = -1. 200 0 O O O O 0 O O O O 0 O
SHEET 1
Max. dE = 0.00700 [eV]
o I
PHS4207T.DAT SIZE SPEC! <MM1*MM2*NM3> where MM1*NH2*MM3 <
12**3 MM1 • 12 NM2 « 12 MH3 • 12
Tl • .060000 0 « .070000 Be ' 400.0
All conflagrations of 12 sheets are exactly of thla type without
exception.
PHS4207T.DAT SIZE SPEC; <MM1*MM2*MM3> where MM1*NM2*HM3 <
12**3 MM1 > 12 MH2 > 12 MM3 ' 12
Tl • .060000 D » .070000 Be > 400.0
--m -.
.1
-
vhere 141Mh143< 123 PHS4207T.DAT SIZl! SPEC; <M1142143>
11111. 12 212 11113 12
l N U D l
where 14114M2M3< 123
n v h u
--a
n u n u - - -
-- a a n
••• T-J MODEL THERMAL CYCLE DATA PLOTTER ••* INPUT FILE NAME t.DAT;
*<C4208T
SIZE SPEC,; <12*12«12> HOLE SPEC; D > .0200 HOPPING SPEC;
TO • .30 eV HOPPING SPEC; Tl • .06 eV coupling J • . 1 eV
* Df STEPS (ONE WAY) • 40, (INITIAL B«ta) ' 100.0 1/eV (deltiBBTA)
« 5 1/eV. WARM UP SWEEPS ' 0; AVERAGING SWEEPS RET to
continue
J - 0.10000 [eV]
J = 0.10000 [eV]
Order Parameter-"]"" Order Parameter £
....
317
[eV) J z 0.10000
. " . . .
- T-J MODEL.THERMAL CYCLR DATA PLOTTER ••• INPUT FILR NAMR
..DAT;-04208T
SIZE SPRC; <121212) HOLI SPRC.; D. .0200 HOPPINO SPRC.; TO .30eY
HOPPINO SPRC.; Tl - .06 eY couplin J.1eY
• of STIP! (ONR WAYI40 (INITIAL Bt1- 100.0 l/eV (deltBITAI l/eV.
WAR UP!WEEPS 0; AVRRA01NO SWRRPS _ I¥IT to contlnue
400
.~.
CORELATIONO 1-3 <. ,«• •—•-"
CORELATION 1-5
CORELATIONO l -
CORELATIONO 1-79 CORELATION 1-79
r1-'•Nvs Radial part
13.117
.~
Phese
CORELATION1-5......T.-
-J
Phase
/ —
^ N ^. - - \ \ \
^ V ~ N \ \ -^ V — —
bond length * 2Eave
CO
I PH342OIT.DAT SIZE SPEC; <MM1*MM2*HM3> where i<Ml*MM2*NM3
< 12«*3 MM1 > 12 MM2 • 12 MM3 • 12
Tl • .060000 D - .020000 Be • 300.0
Highest enerfy sheet
PHS420iT.DAT SIZE SPEC! <MM1*MH2*MM3> where MM1*NM2*MM3 <
12«*3 MM1 • 12 NN2 • 12 MH3 • 12
Tl » .060000 D * .020000 Be • 300.0
~. _.--._.~. ~.r=^.... . ....... "
bond ¥ength = 2E8ve
Mex.dE = 0.05752 [eV]
whcre MMlMM2MM3 < 123
PHS4201T.DAT IIIZI! SPEC: <MM1M2M3) 11M 1 12 MM2 12 1'11'13
12
wh e r e i1M hMM21'13 < 12 3 PHS420T.DAT SIZI! SPI!C:
<111111'11121'13> MMI 12 MM2 12 11M312
l M ω ω l
nvnυ
nvnυ
unHυwnυ
nvwnuu.
eR
SHEET 6
Max. dE = 0. 05752 [eV]
PHS4208T.DAT SIZB SPEC; <MMI*MM2*MM3> where MM1*MM2*MM3 <
12**3 NH1 • 12 MM2 • 1 2 MM • 12
Tl > .060000 P • .020000 Be • 300.0
*** T-J MODEL THERHAL CYCLE DATA PLOTTER **• INPUT FILE NAME *.DAT;
*»G4701T. PAT
SIZE SPEC,; <12*12*12> HOLE SPEC; D • .0060 HOPPING SPEC; TO
• .30 eV HOPPINO SPEC; Tl • .06 eV coupling J > .1 eV
* of STBPS (ONE WAY) • 40, (INITIAL Beta) • 150.0 1/eV (deltlBETA)
- 5 1/eV. WARM UP SWEEPS - 0; AVERAGING SWEEPS RET to
continue
J - 0.10000 [eV]
0.05000 [eV] 50 [1/eV]
"“2123 12
SHEET 6
T-J MODEL THERALCYCLE DATA PLOTTER ••• INPUT FILE
NAE.DAT;.047011'.DAT
SIZE SPEC.; <121212> HOLE SPEC.; D. .0060 HOPPING SPEC.;
TO.30.V HOPPING SPEC.; Tl.06.V coupll nl J. .1.V
4ofSTBPS (ONE WAY)40. INITIAL8.(8)150.0l/eV (4llaBETA) • 5 l/eV.
WARM UP 9WI!EPS 0; AVERAGINO 9WEI!P9 RET to aontlnue
400
J = 0.10000 [eV]
Radial part
CORELATIONO 1-3 CORELATION 1-3
Tt*.Qt
_.....<6
--e .•
...._-~_..;..
...
v
Radial pert
... .
[1/eV]
\ —
\ _ -.
Max. dE = 0.02775 [eV]
PHS4706T.DAT SIZE SPEC; <MM1*MM2*NM3> whtre MN1*MM2*NM3 <
12*»3 MM1 • 12 MH2 • 12 NM3 • 12
Tl • .060000 O • .006000 Be • 36O.0
Loved energy sheet; tnerclet In 12 iheeti range fro* -.5073 to
-.6016. None of conflxurfttIons !• periodic.
PH3*705T.DAT SIZE SPEC; <HM1*HH2*HM3> where MH1*MH2*MH3 <
12**3 MM1 > 12 NH2 - 12 NN3 • 12
Tl > .060000 D - .00600C Be > 360.0
SHEET 1
x.dE = O. 02775 [eV]
wherMMlM2-MM3 < 12..3
PHiU705T. DAT 91ZI! SPEC; <MMlM2M3:' MMl 12 MM2 12 MM3 12
PH14701T. DAT SIZI IPI!C; <MMlMM2MM3> whreN1M2M3 < 12..3
NN1 12
""2 12 MN3 12
l N ω
H
AW
n u n u
a u a u
o
n W A V E -
0
- e D
Max. dE = D. 02775 [eV]
i »*
SHEET 2
ROTATION ANGLE
THETA = 1.750
PHS47O6T.DAT SIZE SPEC; <NM1*MM2*MM3> vhere MM1*MM2*MM3 <
12»»3 HM1 • 12 MM2 • 12 HM3 • 12
Tl • .060000 D • .006000 Be • 350.0
PHS4906T.DAT SIZE SPEC; <NM1*MM2*MM3> where HH1«HH2»MH3 <
12**3 MM1 - 24 MM2 > 24 HH3 • 3
Tl • .000000 D • .070000 Be * 400.0
SHEET 2
Hu
nu
F
‘ E. .. a p a - - 6 . .. a ' a ' a T O ' a
-----e- 4
4
' a ‘ a T a .. a ' a y a a T E . a •.
-F - F - F - - F ι F L
-
-
-
-
-
-
F
F
‘ a a ' a - E B ' a e ' a T a ' a ' s a ' a
-- 4
.‘ JF
‘ dF
----
a ' a a ' a ' a ' s ' a v a ' a ' a a y a
ι--
"
ι F . - ' F - . F ι h F ι - F
a9F
a4
a
.
F
R
h
ι
F
ι
F
'a.
a T S ' a ' a ' s ' a T a f a ' s
a T A
----- J
a
‘ “ ‘ dv
‘ J'
JV
A .--.---
'a.' ‘. ' s ' a . f ' . ' ' a T a ‘ ' a T a s •
h
a ' a a ' a