Spin Liquid Phases?

8/3/2019 Spin Liquid Phases?

1/39

Houches/06//2006

Spin Liquid Phases ?


2/39

Houches/06//2006

Valence Bond Crystals Valence Bond Crystals

A si

mple way to overcome frustration

Crystal of singlets

Fully optimized bonds and absence of m.-f. interactions

How to overcome effect of frustration ?

4-spin S=0 state

J.B.Fouet et al. 2002, W. Brenig 2002

P. Sindzingre 2003, E. Berg et al 2003

LRO in singlet-singlet correl. fonct.

(crystal)

Modes of gapped excitations:

integer(S=1, 0 excitations

A product of singlet wave functions

is a good app. of the N. body g.-s.


3/39

Houches/06//2006

Quantum Spin Liquids

No spin-spin long range order

Singlet-singlet long range order

Gapful spin integer excitations

No LRO in spins

No LRO in dimers

and in any local correlation fctn

Specificity of the g.-s. w.-f.

Fractionalized spin excitations

may be gapful or gapless

Valence Bond Crystals

e T(

wG


4/39

Houches/06//2006

Quantum Spin LiquidsResonating Valence Bond Liquids

+

EN )21( E+ terms

P.W. Anderson, L. Balents,

V. Elser, M.P.A. Fisher,

E. Fradkin, S. Kivelson,

C.L., G. Misguich,

R. Moessner, S. L. Sondhi

V. Pasquier, N. Read,D. Rokhsar, D. Sutherland, S.

Sachdev, S. Senthil,

D. Serban, P. Sindzingre

.


5/39

Houches/06//2006


+

EN )21( E+ terms

No LRO in any local correlation

fonctions (liquid) , spin gap


6/39

Houches/06//2006


+

EN )21( E+ terms


fonctions (liquid), spin gap

Continuum of gapped unconfined

spin excitations (spinons)

By alphabetic order:

P.W. Anderson,

L. Balents,

M.P.A. Fisher,

E. Fradkin,

S. Kivelson,N. Read,

S. Sachdev,

S. Senthil..


7/39

Houches/06//2006

confined spinons in the

V-B crystal

unconfined spinons in

the R.V.B. Spin Liquids


8/39

Houches/06//2006


+

EN )21( E+ terms






9/39

Houches/06//2006


+

EN )21( E+ terms





Subtle phase coherence properties

(Quantum liquid)

and S=0 visons excitations

An exactly solvable

dimer liquid model

Ising gauge theory

G. Misguich et al. 02


10/39

Houches/06//2006

Misguich et aldimer model (02)

only kinetic energy: sum from 3 to six dimer moves around eachhexagon of the kagome lattice

3

6

4

H = 7 dimer moves from black to red config. + h.c.


11/39

Houches/06//2006

Misguich et aldimer model (02)

only kinetic energy: sum from 3 to six dimer moves around eachhexagon of the kagome lattice

3

6

4

H = 7 dimer moves from black to red config. + h.c.

3

6

4

H


12/39

Houches/06//2006

Coherence Effects and S=0 Visons excitationsG. Misguich V. Pasquier & D. Serban P.R.L.02

The Resonating Valence Bond ground-state:

+ .++


13/39

Houches/06//2006

Coherence Effects and S=0 Visons excitationsG. Misguich V. Pasquier & D. Serban P.R.L.02

The Resonating Valence Bond ground-state:

b

a

An S=0 gapped excitation: the two-visons wave-function

.+-

+ .++


14/39

Houches/06//2006


+

EN )21( E+ terms


fonctions (liquid)




(Quantum liquid)

and S=0 gapped visons excitations

Topological degeneracy


15/39

Houches/06//2006

MSE Spin Liquid Spin gap & Topological degeneracy


16/39

Houches/06//2006



17/39

Houches/06//2006



18/39

Houches/06//2006



19/39

Houches/06//2006

Topological degeneracy in SRRVB Spin

Liquids

a generic g.-s. configuration


20/39

Houches/06//2006


Liquids


draw an arbitrary cut


21/39

Houches/06//2006


Liquids

;x= 3


draw an arbitrary cut

count the number of dimers

across the cut


22/39

Houches/06//2006


Liquids

;x= 3 ;

x=1

Pijkl


23/39

Houches/06//2006


Liquids

;x= 3 ;

x=1

Parities of winding numbers (;x,;y) are good quantum numbers:

4 unconnected topological subspaces on a 2-torus

degenerate in the thermodynamic limit

Pijkl


24/39

Houches/06//2006


Liquids

;x= 3 ;

x=1




4-fold degeneracy of low lying singlets

Pijkl


25/39

Houches/06//2006


Liquids

;x= 3 ;

x=1




4-fold degeneracy of low lying singlets

A topological quantum bit (Kitaev quant-phys/9707021) ?

Pijkl


26/39

Houches/06//2006


+

EN )21( E+ terms


fonctions (liquid)




(Quantum liquid)



A topological quantum-bitA. Y. Kitaev 97, 03

L. Ioffe and coll. 02

G. Misguich et al 04


27/39

Houches/06//2006


+

EN )21( E+ terms


fonctions (liquid)




(Quantum liquid)



A topological quantum-bit

What seems the most favorable

conditions to observe

Quantum Spin Liquids?

triangular geometry

importance of effective kinetic

terms acting coherently on

more than two spins


28/39

Houches/06//2006

H = t ++ + ...+ ... + V

on the triangular lattice 00

MoessnerSondhi hard core quantum dimer model

V / t0 1

12 x 12 SRRVBVBC VBC

On the square lattice the original model due to Rokhsar & Kivelson

has no real spin liquid phase only a Q.C. point


29/39

Houches/06//2006

Kagom-like ?

SR-RVB

Gapless LR-RVB ?

H = 2 J2 7< i,j> Si . Sj+ J4 7 (Pijkl+ P-1

ijkl )

on the triangular lattice


30/39

Houches/06//2006

Quantum behavior of models with

infinite local degeneracy in the

classical limitHeisenberg model on the kagom

checkerboard and pyrochlore lattices

Half integer odd spins versus integer ones


31/39

Houches/06//2006


32/39

Houches/06//2006

Classical Heisenberg Hamiltonian on

the kagom lattice

An infinite number of soft modes, an infinite T=0 degeneracy

Same property on the checkerboard lattice, or the pyrochlore lattice


33/39

Houches/06//2006

Quantum ground-state and first excitations

of the Heisenberg model on the kagom lattice

have a total spin S=0

A gap < 10 -3 in the singlet

sector(if any)!

Very large extensive entropy

from singlets at ultra-low T

A small spin gap (~1/20)

At low temperature Cv is insensitive to large magnetic fields

( Sindzingre et al.. PRL 00 , Ramirez et al.. PRL 00)

pTCv!butT(w )exp(G


34/39

Houches/06//2006

Spin-3/2 kagom Antiferromagnet

No theoretical results

Experiments: the spin liquid picture is plausible.

Some features are very much alike the spin-1/2 system

Dynamics of spins (Uemura et al 1994)

Low lying local singlet excitations (Ramirez et al. 2000)

A very tiny spin gap if any (Ramirez et al, Bono, Mendels et al.)

Quasi-critical behavior of the spin susceptibility atintermediate temperatures (C. Mondelli, H. Mutka and coll.

2002, A. Georges and coll. 2001)


35/39

Houches/06//2006

Conclusion

SU(2) magnets in 2d

Semi-classical Nel phases

Quantum phases: Valence Bond Crystals and Spin

Liquids

Quantum Spin Liquids

A Realistic Spin Liquid : MSE on triangular latt.

Open question: spin-1/2-Heisenberg model on the

kagom lattice. A true new phase or a system near aQ.C. point?

Half-odd integer spins versus integer ones


36/39

Houches/06//2006

A toy model for a topological quantum-bitG. Misguich, V. Pasquier, F. Mila, C.L. cond-mat/0410693

Z2 spin liquid on a cylinder: 2-fold degenerate g.s.

a topological q-bit

protected from any local perturbations

How write and read it?


37/39

Houches/06//2006



a topological q-bit




38/39

Houches/06//2006



a topological q-bit



Introduce a local perturbation

which change the geometry

from a cylinder to a plane


39/39

Houches/06//2006



a topological q-bit



gap

perturbationVc

exp(-L)

1/L

Date post:	06-Apr-2018
Category:	Documents
Upload:	konnasder
View:	223 times
Download:	0 times

Spin Liquid Phases?

Documents