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Spin-orbital seperation in 1-D
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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Spin-orbital seperation in 1-D
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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Spin-orbital seperation in 1-D
Selected References
A good extensive reference for Physics in 1-D:
T. Giamarchi, Quantum Physics in One dimension, Oxford
Science Publications (2004).
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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Spin-orbital seperation in 1-D
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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Spin-orbital seperation in 1-D
Introduction
1 Introduction
2 Spin-Charge seperation
The mechanism
The experiment
3 Orbiton in 1-d
The mechanism
The experiment
4 Kugel-Khomskii model and its exact solution
5 Future directions
Spin orbital seperation in 1 D
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Spin-orbital seperation in 1-D
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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Spin-orbital seperation in 1-D
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.Magnons, phonons fractionally charged particles in
Quantum Hall Systems are few common examples.
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Spin-orbital seperation in 1-D
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.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 orbital seperation in 1 D
Spin-Charge seperation
1 Introduction
2 Spin-Charge seperation
The mechanism
The experiment
3 Orbiton in 1-d
The mechanism
The experiment
4 Kugel-Khomskii model and its exact solution
5 Future directions
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Spin orbital seperation in 1 D
Spin-Charge seperation
The mechanism
Table of Contents
1 Introduction
2 Spin-Charge seperation
The mechanism
The experiment
3 Orbiton in 1-d
The mechanism
The experiment
4 Kugel-Khomskii model and its exact solution
5 Future directions
Spin-orbital seperation in 1-D
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p p
Spin-Charge seperation
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
Spin-Charge seperation
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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Spin-Charge seperation
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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Spin-Charge seperation
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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Spin-orbital seperation in 1-D
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Spin-Charge seperation
The experiment
Table of Contents
1 Introduction
2 Spin-Charge seperation
The mechanism
The experiment
3 Orbiton in 1-d
The mechanism
The experiment
4 Kugel-Khomskii model and its exact solution
5 Future directions
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Spin-Charge seperation
The experiment
Spectral function A(, k) is the probability to find a statewith frequency and momentum k.
Spin-orbital seperation in 1-D
S C
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Spin-Charge seperation
The experiment
Spectral function A(, k) is the probability to find a statewith frequency and momentum k.
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.
Spin-orbital seperation in 1-D
S i Ch ti
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Spin-Charge seperation
The experiment
Spectral function A(, k) is the probability to find a statewith frequency and momentum k.
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-orbital seperation in 1-D
Spin Charge seperation
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Spin-Charge seperation
The experiment
Material for experimental investigation
SrCuO2 is a quasi-1-d compound with
very weak interchain hopping.
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Spin Charge seperation
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Spin-Charge seperation
The experiment
Material for experimental investigation
SrCuO2 is a quasi-1-d compound with
very weak interchain hopping.
It can be mapped to 1-d t-J model dueto large onsite repulsion.
Spin-orbital seperation in 1-D
Spin-Charge seperation
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Spin-Charge seperation
The experiment
Material for experimental investigation
SrCuO2 is a quasi-1-d compound with
very weak interchain hopping.
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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Spin Charge seperation
The experiment
C. Kim et,al (1996) obtained
the ARPES spectrum ofSrCuO2.
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Spin Charge seperation
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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Spin-Charge seperation
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p g p
The experiment
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Spin-Charge seperation
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The experiment
The spectrum produced broad features expected from t-J
model calculations.
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Spin-Charge seperation
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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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Spin-Charge seperation
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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.
Spin-orbital seperation in 1-D
Orbiton in 1-d
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1
Introduction
2 Spin-Charge seperation
The mechanism
The experiment
3 Orbiton in 1-d
The mechanism
The experiment
4 Kugel-Khomskii model and its exact solution
5 Future directions
Spin-orbital seperation in 1-DOrbiton in 1-d
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The mechanism
Table of Contents
1 Introduction
2 Spin-Charge seperation
The mechanism
The experiment
3 Orbiton in 1-d
The mechanism
The experiment
4 Kugel-Khomskii model and its exact solution
5 Future directions
Spin-orbital seperation in 1-DOrbiton in 1-d
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.
Spin-orbital seperation in 1-DOrbiton in 1-d
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.
Spin-orbital seperation in 1-DOrbiton in 1-d
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.
Spin-orbital seperation in 1-DOrbiton in 1-d
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.
Spin-orbital seperation in 1-DOrbiton in 1-d
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.
Spin-orbital seperation in 1-DOrbiton in 1-d
The experiment
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The experiment
Table of Contents
1 Introduction
2 Spin-Charge seperation
The mechanism
The experiment
3 Orbiton in 1-d
The mechanism
The experiment
4 Kugel-Khomskii model and its exact solution
5 Future directions
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Spin-orbital seperation in 1-DOrbiton in 1-d
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.
Spin-orbital seperation in 1-DOrbiton in 1-d
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.
Spin-orbital seperation in 1-DOrbiton in 1-d
The experiment
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Coupling mechanism in the RIXS experiment.
3dx2y2 and 3dxz states are coupled primarily.
Spin-orbital seperation in 1-DOrbiton in 1-d
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) !
Spin-orbital seperation in 1-DOrbiton in 1-d
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.
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Spin-orbital seperation in 1-DOrbiton in 1-d
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
2 Spin-Charge seperation
The mechanism
The experiment
3 Orbiton in 1-d
The mechanism
The experiment
4 Kugel-Khomskii model and its exact solution
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-
Spin-orbital seperation in 1-D
Kugel-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-
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.
Spin-orbital seperation in 1-D
Kugel-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-
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.
Spin-orbital seperation in 1-D
Future directions
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1 Introduction
2 Spin-Charge seperation
The mechanism
The experiment
3 Orbiton in 1-d
The mechanism
The experiment
4 Kugel-Khomskii model and its exact solution
5 Future directions
Spin-orbital seperation in 1-D
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.
Spin-orbital seperation in 1-D
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.
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.
Spin-orbital seperation in 1-D
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.
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.
Spin-orbital seperation in 1-D
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?
Spin-orbital seperation in 1-D
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?
A boon to Quantum Computing ?
One roadblock in Quantum Computing is decoherence .
Spin-orbital seperation in 1-D
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?
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
Spin-orbital seperation in 1-D
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.
Spin-orbital seperation in 1-D
Future directions
Selected References
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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).
Spin-orbital seperation in 1-D
Future directions
Selected References
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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).
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-orbital seperation in 1-D
Future directions
Selected References
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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).
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).
Spin-orbital seperation in 1-D
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.
Spin-orbital seperation in 1-D
Future directions
Acknowledgements
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Acknowledgements
Thanks to my advisor Prof. Diptiman Sen for discussions.
Thanks to QCMJC without which I would not have gone
through many of these papers in detail and give this talk.
Spin-orbital seperation in 1-D
Future directions
Acknowledgements
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Acknowledgements
Thanks to my advisor Prof. Diptiman Sen for discussions.
Thanks to QCMJC without which I would not have gone
through many of these papers in detail and give this talk.
Thanks to audience for patient presence and listening.
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