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Exact ground states of a frustrated 2D magnet: deconfined fractional excitations at a first order quantum phase transition. Cristian D. Batista and Stuart A. Trugman T-11 Los Alamos National Laboratory Los Alamos, NM - USA. Cond-mat/047216. Outline. -General Motivation.

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Exact ground states of a frustrated 2D magnet: deconfined fractional excitations at a first order quantum phase transition

Cristian D. Batista and Stuart A. Trugman

T-11

Los Alamos National Laboratory

Los Alamos, NM - USA

Cond-mat/047216


Outline fractional excitations at a first order quantum phase transition

-General Motivation.

-Model for a frustrated 2D Magnet.

-Exact Ground States: Valence bond crystal with

soft 1D topological defects.

-Excitations:Spinons propagating along 1D paths.

Spin charge separation for one hole added.

-Identification of the solvable point with a first

order QPT.

-Extensions to other 2D lattices.

-Conclusions.


Introduction fractional excitations at a first order quantum phase transition

H= J1 Si .Sj + J2  Si .Sj

i , j i , j

AFM

AFM

(, )

(,)

Valence Bond Crystal ( N. Read and S. Sachdev,

Phys. Rev. Lett. 66, 1773 (1991).)

O.P.

?

J2 /J1

1/2

Uniform Spin Liquid (P. Fazekas and P. W. Anderson,

Philos. Mag. 80, 1483 (1974).)


Introduction fractional excitations at a first order quantum phase transition

Proposals for deconfined points

in frustrated magnets

O.P.

O.P.

H= Jij Si.Sj + …

Roksar-Kivelson model

VBC I

AF

VBC

VBC II

g

QCP

QCP

T. Senthil et al, Science 303, 1490 (2003)

Moessner et al, Phys.Rev. B65 024504(2002)

E. Fradkin et al, Phys. Rev.B69, 224415 (2004)

A. Vishwanath et al, Phys. Rev.B69, 224416 (2004)


Introduction fractional excitations at a first order quantum phase transition

AFM

AFM

(, )

(,)

Proposals for deconfined points

in frustrated magnets

Confederate Flag model

VBC I

VBC II

0

x

QCP

A.M. Tsvelik, cond-mat/0404541 (2004)

A.A. Neresyan and A. M. Tsvelik, Phys. Rev. B 67, 024422 (2003)


Hamiltonian fractional excitations at a first order quantum phase transition

H= J1 Si .Sj + J2  Si .Sj

+ K  (Pij Pkl+ Pjk Pil+ Pik Pjl)

i , j i , j

     

i

j

This sign is negative

in the usual four-cyclic

exchange term.

k

l


Hamiltonian fractional excitations at a first order quantum phase transition

Hp=(3J1 /2) P

Hp=H(J2=J1 /2, K=J1 /8)

P  is the projector on the S =2 subspace.

S   1

= singlet dimer


Ground States fractional excitations at a first order quantum phase transition


Ground States: Defects fractional excitations at a first order quantum phase transition


Ground States: Defects fractional excitations at a first order quantum phase transition


Low Energy Excitations fractional excitations at a first order quantum phase transition

x

x

x

x

x

x

x

x

Deconfined

Confined


Low Energy Excitations fractional excitations at a first order quantum phase transition

x

x

x

x

x

x

x

x

Doped System: Spin-Charge separation


First Order Quantum Phase Transition fractional excitations at a first order quantum phase transition

4-fold degeneracy

8-fold degeneracy

OP

ZD

SD

0

g


General Transition fractional excitations at a first order quantum phase transition

Ol+1

Ol

Ol+2

Ol+4

Ol +3

Ol+5 …..

. . . . .

. . . . .

-

-

-

-

-

-

-

q=0


General Transition fractional excitations at a first order quantum phase transition

Ol+1

Ol

Ol+2

Ol+4

Ol +3

Ol+5 …..

. . . . .

. . . . .

+

+

+

+

+

+

+

q=


Extensions to other Lattices fractional excitations at a first order quantum phase transition

Hp= Q ,

where Q is the projector on the S=2,3 subspace.


Conclusions: fractional excitations at a first order quantum phase transition

A Valence Bond Crystal is exactly obtained for the fully frustrated Heisenberg model on a square lattice in the presence of a small four-spin term (K=J1/8).

The ground states and the excitations exhibit exotic behaviors like the softening of 1D topological defects and the emergence of deconfined spinons.

This point can be identified with a first order QPT.


Conclusions: fractional excitations at a first order quantum phase transition

There is spin-charge separation when the system is doped with one hole.

The common origin of the exotic behaviors is a dynamical decoupling of the 2D magnet into 1D systems.

Questions:

Finite concentration of holes and anisotropic conductivity?

Effect of finite temperature?

- What is the effect of reducing K?


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