Spin-orbital separation in 1-D

7/31/2019 Spin-orbital separation in 1-D

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Spin-orbital seperation in 1-D


Abhiram Soori

Quantum Condensed Matter Journal ClubDepartment of Physics

Indian Institute of ScienceBangalore

REFERENCE-J Schlappa et al., Nature, 485, 82 (2012).

12th June 2012
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Selected References

A good extensive reference for Physics in 1-D:

T. Giamarchi, Quantum Physics in One dimension, Oxford

Science Publications (2004).
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Selected References




Spin Charge separation:E.H. Lieb and F.Y. Wu, Phys. Rev. Lett., 20, 1445 (1968).

C. Kim et al., Phys. Rev. Lett., 77, 4054 (1996).

B.J. Kim et al., Nature Phys., 2, 397 (2006).

O. M. Auslaender et al., Science, 308, 88 (2005).

Y. Jompol et al., Science, 325, 597 (2009).T.L. Schmidt et al., Phys. Rev. B., 82, 245104, (2010).

Spin Orbiton Separation:

J Schlappa et al., Nature, 485, 82 (2012).

Brijesh Kumar, arXiv: 1205.6436 (2012).
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Outline

1 Introduction

2 Spin-Charge seperation

The mechanismThe experiment

3 Orbiton in 1-d

The mechanism

The experiment

4 Kugel-Khomskii model and its exact solution

5 Future directions

S i bit l ti i 1 D
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Introduction

1 Introduction


The mechanism

The experiment

3 Orbiton in 1-d

The mechanism

The experiment


5 Future directions

Spin orbital seperation in 1 D
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Introduction

One of the interesting consequences of Many-bodyPhysics is the emergence of new elementary excitations or

new particles.

These new particles arise due to the collective behavior of

the constituent fundamental particles i.e., electrons.

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Introduction


new particles.


the constituent fundamental particles i.e., electrons.Magnons, phonons fractionally charged particles in

Quantum Hall Systems are few common examples.

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Introduction


new particles.


the constituent fundamental particles i.e., electrons.Magnons, phonons fractionally charged particles in

Quantum Hall Systems are few common examples.

In d > 1 dimensions, Landau Fermi Liquid theory workswell with Landau quasi-particles as the elementary

excitations.

However, the elementary excitations of interacting electron

system in 1-d, are spinons and holons(chargons).



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Spin-Charge seperation

1 Introduction


The mechanism

The experiment

3 Orbiton in 1-d

The mechanism

The experiment


5 Future directions



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The mechanism

Table of Contents

1 Introduction


The mechanism

The experiment

3 Orbiton in 1-d

The mechanism

The experiment


5 Future directions



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p p


The mechanism

Spinons: Each spinon has a spin 1/2 and no charge.

Figure: Spinons in a spin chain: Upper chain is GS - AF-ordered(S = 0). Lower one contains two spinons spatially separated(S = 1).



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p p


The mechanism

Spinons: Each spinon has a spin 1/2 and no charge.

Figure: Spinons in a spin chain: Upper chain is GS - AF-ordered(S = 0). Lower one contains two spinons spatially separated(S = 1).

Holons: Each holon has a charge +e, but no spin.

Figure: Pure holon looks like this.


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The mechanism

Though spin-charge separation was first theoreticallyshown as early as 1968 (Lieb and Wu, PRL, 20, 1445), the

first experimental evidence came in 1996 (Kim et al., PRL,

77, 4054).

It is quite challenging to probe spin charge separation in a

transport experiment.

An attempt for spin charge separation in a simple setup

that consists of a quantum wire connected to leads fails.

Because, it is the electron that reconstitutes from spin and

holon that hops on to the lead rather than the spinon andholon separately !

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The mechanism

Though spin-charge separation was first theoreticallyshown as early as 1968 (Lieb and Wu, PRL, 20, 1445), the

first experimental evidence came in 1996 (Kim et al., PRL,

77, 4054).

It is quite challenging to probe spin charge separation in a

transport experiment.

An attempt for spin charge separation in a simple setup

that consists of a quantum wire connected to leads fails.

Because, it is the electron that reconstitutes from spin and

holon that hops on to the lead rather than the spinon andholon separately !

A direct way would be to remove/add an electron to the

system and look for spin charge separation.
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The experiment

Table of Contents

1 Introduction


The mechanism

The experiment

3 Orbiton in 1-d

The mechanism

The experiment


5 Future directions



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The experiment

Spectral function A(, k) is the probability to find a statewith frequency and momentum k.


S C


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The experiment


ARPES (Angle Resolved Photoemmision Spectroscopy) isthe experimental technique to observe the excitations in

solids. It can give the information about energy and

momentum of the electrons/excitations in solids.


S i Ch ti


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The experiment


ARPES (Angle Resolved Photoemmision Spectroscopy) isthe experimental technique to observe the excitations in

solids. It can give the information about energy and

momentum of the electrons/excitations in solids.

In a spectroscopic (ARPES) experiment, two branches of

spectrum confirm the spin-charge separation.

Figure: Courtsey:Wikipedia


Spin Charge seperation


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The experiment

Material for experimental investigation

SrCuO2 is a quasi-1-d compound with

very weak interchain hopping.


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The experiment




It can be mapped to 1-d t-J model dueto large onsite repulsion.


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The experiment




It can be mapped to 1-d t-J model dueto large onsite repulsion.

Holon energy scale t and Spinon

energy scale J in this compund can be

obtained from neutron scattering and

Optical techniques as well as from first

principle calculations.


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The experiment

C. Kim et,al (1996) obtained

the ARPES spectrum ofSrCuO2.


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The experiment

C. Kim et,al (1996) obtained

the ARPES spectrum ofSrCuO2.

Using the known values of t

and J for Sr2CuO3, they

calculated Spectral functionA(k, ), Charge and Spincorrelation functions N(q, )and S(q, ).
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p g p

The experiment


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The experiment

The spectrum produced broad features expected from t-J

model calculations.
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The experiment

Analysis of peaks (inset: Bethe

Ansatz Calculation).Experiment

The ARPES spectrum of B.J. Kim (2006) showed the clear

peaks expected from theory.


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The experiment

Analysis of peaks (inset: Bethe

Ansatz Calculation).Experiment

The ARPES spectrum of B.J. Kim (2006) showed the clear

peaks expected from theory.

Also, the reason why the peaks were blurred in earlier

(1996) experiment was explained.


Orbiton in 1-d
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1

Introduction


The mechanism

The experiment

3 Orbiton in 1-d

The mechanism

The experiment


5 Future directions

Spin-orbital seperation in 1-DOrbiton in 1-d
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The mechanism

Table of Contents

1 Introduction


The mechanism

The experiment

3 Orbiton in 1-d

The mechanism

The experiment


5 Future directions


Th h i
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The mechanism

Orbitons can arise in 1-d AF spin chains that have an extra

orbital degree of freedom.


Th h i
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The mechanism

Orbitons can arise in 1-d AF spin chains that have an extra

orbital degree of freedom.The compound Sr2CuO3 is a quasi-1-D material with CuO4plaquettes arranged in a chain.

Figure: Particles occupy 3d x2 y2 orbitals. Large AF coupling(J 250meV) renders the chain an AF spin-1/2 Heisenbergchain.


The mechanism


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The mechanism

Cu is in 3d9 configuration one

hole state (called particle).

Large onsite U drives the system

into a Mott-insulating state.


The mechanism
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The mechanism

Cu is in 3d9 configuration one

hole state (called particle).

Large onsite U drives the system

into a Mott-insulating state.

So, one hole is in 3d orbital

(non-degenerate).

At the moment it can occupy one

of the two spin degenerate

states.


The mechanism
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The mechanism

Figure: Spin-orbital separation

Coupling these orbitals to EM-radiation of the right frequency

can couple two orbitals giving an extra (the orbital) degree of

freedom.


The experiment
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The experiment

Table of Contents

1 Introduction


The mechanism

The experiment

3 Orbiton in 1-d

The mechanism

The experiment


5 Future directions
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The experiment


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p

Unlike photo-emission, to observe spin-orbiton separation,

an electron at a site can be excited to another orbital and

the subsequent separation of spinon and orbiton can be

looked for.

The experimental technique to this is called resonantinelastic X-ray scattering (RIXS).

An incident photon excites the electron in a particular level

to an excited state and emits as another photon.


The experiment
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Unlike photo-emission, to observe spin-orbiton separation,

an electron at a site can be excited to another orbital and

the subsequent separation of spinon and orbiton can be

looked for.

The experimental technique to this is called resonantinelastic X-ray scattering (RIXS).

An incident photon excites the electron in a particular level

to an excited state and emits as another photon.

The energy, momentum and spin of the excitations can befound to a good precision.


The experiment
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Coupling mechanism in the RIXS experiment.

3dx2y2 and 3dxz states are coupled primarily.


The experiment
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The spectrum shows spin-orbiton separation.

The spin segment of the spectrum confirms the

theoretically predicted spin dynamical structure factor.Further, the continuum of spin excitation has two

boundaries with periods and 2 implying that the spinonis created out of the initial zero-spin excitation. (Fadeev

and Takhtajan - 1981) !


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The spectrum agrees well with the theoretical calculations.

a) Experiment, b)Lower and Upper edges of orbiton, c) Theory.


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The experiment


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The spectrum agrees well with the theoretical calculations.

a) Experiment, b)Lower and Upper edges of orbiton, c) Theory.

Kugel-Khomskii (KK) model for Sr2CuO3:

H =

JOj, (c

j,cj+1, + h.c.) + J

j

SjSj+1 + E0nj

Authors argue that the above Hamiltonian is identical to 1D

t-J model and hence theoretically spin-orbiton separation

follows, orbiton taking the role of holon!

Spin-orbital seperation in 1-DKugel-Khomskii model and its exact solution
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1 Introduction


The mechanism

The experiment

3 Orbiton in 1-d

The mechanism

The experiment


5 Future directions

Spin-orbital seperation in 1-DKugel-Khomskii model and its exact solution
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A recent theory (arXiv: 1205.6436) paper gives exact solution ofspin-orbiton separation with a special case of KK model-


Kugel-Khomskii model and its exact solution
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KK model for Sr2CuO3:

H =l

[Jzz

l

z

l+1

+JXl,l+1(x

l

x

l+1

+y

l

y

l+1

)+Jl l+1+z

l

]

where Xl,l+1 = (1 + l l+1)/2; is orbital-pseudo-spin.


Kugel-Khomskii model and its exact solution
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KK model for Sr2CuO3:

H =l

[Jzz

l

z

l+

1

+JXl,l+1(x

l

x

l+

1

+y

l

y

l+1

)+Jl l+1+z

l

]

where Xl,l+1 = (1 + l l+1)/2; is orbital-pseudo-spin.

Above paper solves the case with J = 0.


Future directions


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1 Introduction


The mechanism

The experiment

3 Orbiton in 1-d

The mechanism

The experiment


5 Future directions


Future directions


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All the orbiton-peaks are not clearly visible in the ARPESspectrum. Future experiments could aim at more distinct

peaks.


Future directions
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peaks.

There are unaccounted spectral weights in the

experimental results. Some of these have beenqualitatively speculated to come from terms disregarded in

theoretical models such as next-nearest neighbor hopping,

coupling to phonons and temperature.


Future directions
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peaks.

There are unaccounted spectral weights in the

experimental results. Some of these have beenqualitatively speculated to come from terms disregarded in

theoretical models such as next-nearest neighbor hopping,

coupling to phonons and temperature.

Kugel-Khomskii model with Jl l+1 term may be aninteresting problem to look at.


Future directions


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Spin-charge-orbiton separation ?Is is possible to produce spinon, holon and orbiton at the

same time in a single set-up?


Future directions


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A boon to Quantum Computing ?

One roadblock in Quantum Computing is decoherence .


Future directions


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A boon to Quantum Computing ?

One roadblock in Quantum Computing is decoherence .

The orbital transitions are fast ( 1015 seconds),

compared to orbiton decoherence time ( 1014 seconds).

This hints at possible application of orbital degree of

freedom in realizing Quantum computer.

Nature News - doi:10.1038/nature.2012.10471


Future directions

Understanding orbiton is expected to give some useful tips in


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Understanding orbiton is expected to give some useful tips in

understanding of the theories on high-Tc superconductivity in

pnictides and CuO2 based materials.


Future directions

Selected References


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Selected References





Future directions

Selected References


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Selected References




Spin Charge separation:

E.H. Lieb and F.Y. Wu, Phys. Rev. Lett., 20, 1445 (1968).C. Kim et al., Phys. Rev. Lett., 77, 4054 (1996).



Y. Jompol et al., Science, 325, 597 (2009).

T.L. Schmidt et al., Phys. Rev. B., 82, 245104, (2010).


Future directions

Selected References


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Selected References




Spin Charge separation:

E.H. Lieb and F.Y. Wu, Phys. Rev. Lett., 20, 1445 (1968).C. Kim et al., Phys. Rev. Lett., 77, 4054 (1996).



Y. Jompol et al., Science, 325, 597 (2009).

T.L. Schmidt et al., Phys. Rev. B., 82, 245104, (2010).

Spin Orbiton Separation:

J Schlappa et al., Nature, 485, 82 (2012).

Brijesh Kumar, arXiv: 1205.6436 (2012).


Future directions

Acknowledgements


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Acknowledgements

Thanks to QCMJC without which I would not have gone

through many of these papers in detail and give this talk.


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Acknowledgements


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Acknowledgements

Thanks to my advisor Prof. Diptiman Sen for discussions.




Future directions

Acknowledgements


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Acknowledgements

Thanks to my advisor Prof. Diptiman Sen for discussions.



Thanks to audience for patient presence and listening.

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Spin-orbital separation in 1-D