Topological excitations and phase transition hierarchy in strongly correlated electronic systems

Physica C 162-164 (1989) 791-792 North-Hollafid

TOPOLOGICAL EXCITATIONS AND PHASE TRANSITION HIERARCHY IN STRONGLY CORRELATED ELECTRONIC SYSTEMS Alexander PROTOGENOV Institute of Applied Physics, Academy of Sciences of the USSR, 46 Uljanov St., 603600 Gorky, USSR

The ground state structure and topological properties of CO' field with txnite action and a fractional charge are considered in 2+I system of strogly correlated particles. It is concluded that a holon and a spinon are different states of an anyon. To describe the phase structure of the antiferromagnetic Heisenberg model with the Chern-Simons term I introduce the lattice loop model mapped into discrete Gaussian Z model of an effective spin with frustrations. At low P temperatures there is an electric charge Bose condensate, in the intermediate temperature region there exists a Coulomb phase with long-ranqe interactions and at high temperatures there is a confinement phase of topological charges (magnetic charge Bose condensate) and phases of oblique confinement of dyons. where

A

1. I N T R O D U C T I O N The

topological

gauge

theory

berg

antiferromagnet

influence this

of

excitations

on

2+l-dimensional

the

system.

The

strong

spin

since

is small, energy

the

than be

the

the

the

produced

finite

motion

unity,

i.e.

charge

properties

of

n = 8/S are

is the

ground

similar

lattice.

I shall

structure

low-energy

a

and

elementary

confinement invariant where

functional

2.

case model

SPIN

U6/t<<1

CORRELATIONS

long

wave

and

of

the

in CP I r e p r e s e n t a t i o n

has

S = Idx d 2 x

the a c t i o n

limit

2 I { k=I[--~l(~p

+ i A o ( I z k 12 - l - v [ V

in the Hubbard

the

form

+

(1)

x A]z)}

0921-4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

a

a quantum

o~

the

and

zk

action

and

a fractional

A tp(r) = m / 2 , r

Wilczek

and

orbital

momentum

called

Hopf

was

state

Ginzburg-Lanwith

quantum

and

the

GL Hal]

the field

composite (r)

the

expression

motion

yield

parameter

A@(r)

from

coincides

of

condition

the

nonzero

The whole

equations

of

symmetry

superconducting

which

the

quantum

transition

configurations

field

2 + iAp)ZkI

flux

f u n c t i o n a l 2 for a f r a c t i o n a l

The

is

number

characterizes

with

the

be c o n s i d e r e d

O

tlle

spontaneous

state into

the

Sa

"-

the

term

of

can

constraint

the

is

phase

dau

effect.

In

is

it is a b s e n £ .

excitations.

STRONG

at

S A

of

(n 2 = I);

density,

q

mechanism

breakdown

I,

v= 8/21,= p/q

p

imaginary

phase

state

contain

S =

angle ;

The

field

localization

variables;

and

gauge

~z2 Iz =

dimensionless

vacuum

action I .

is m u c h

the

= z+oz,

spin

number.

interaction

and

state

~Zl 12 +

particles

of q u a s i p a r t i c l e s

ground

by

condition

soliton-

energy

the

by

auxiliary

produced

of p a r t i c l e s

the

inhomogeneous

Wigner

consider

of

of

of e x c i -

forms

with

free

superstructure to

space,

the d e n s i t y

ratio

to the

larger can

properties

correlation

quasiparticles fact,

Heisen-

an e s s e n t i a l

delocalization

in m o m e n t u m

like

have

phase

tations

In

in the

is the

P

with

order finite

charge. The

gauge

introduced

by

anyons.

Here

of a h o l e . A n

m is the

anyon

as a

A. Protogenov / Topological excitations and phase transition hierarchy

792

particle quanta

is

and

vortex. the

vortex

]:n t h e

wave

at

a

p charges

singular

function

permutation

=exp(iS)

fermion

(holon)

the

at

(spinon)

anyon-spinon

charge

factor

The limits

is z e r o

tum

fluctuations.

the

rotation

the

the

prefer

corresponds to

-1.

loop

are

motion

limit

"spin"

and

the take

caused

into

by

compact

loop

proves

to

be

leads

to

a

Gaussian S = ~I

model

model

phase

proper-

account

into

holes

quan-

around

a

exist:

a)

pairs

the

with

m=1

c)

from a site

+I.

If t h e

counterwise, effective

inside spin

spin

violation

directions,

of

the

etc.

We

right

c(,ntacts, of

Iz kl
from

the confinement plasma

interme-

the

and

increasing

plasma

due

phase

with

with

m=

m

this

and of

of

electrical

large

phase

in

the

and

T.

At

is s e p a r a t e d

phase

by

an

Phys.

Rev.

addi-

state.

REFERENCES I

P.B.

Wiegmann,

(1988)

S.M.

Lett.

60

821.

Girvin,

Effect

in:

The

Quantum

(Springer-Verlag,

Hall

N e w York,

1986).

continued

J.

Jose

et al.

Phys.

Rev.

16B

(1977)

1217.

8 term. J.

H,~I~CA~z'-2~fMK~x~ )2 + iPk)i n k z k +

Cardy

Phys.

and

205B

FS5

E.

Rabinovici,

(1982)

Nucl.

I.

(2) + _ip8_8 E e M v e k l ( A H Z k _ 2 , M M k ) 32~2 The variables

(~vZl_2,.Mvl)

the

spin

J.

Cardy,

(1982)

z k ( r ) = 0 , 1 , . . .,p-1

Eq. (2) a s s i g n i n g

I

to n o n z e r o

confinement

region

0<8<211

at

plasma

dipoles

charges

n in t h e

m=O

violate

of P p a r i t y

and

tional

by

d)oblique

p)4

n=1, and

the m o d e l

non-variant

periodically with

large to 0 or

tile f r u s t r a t i o n s

choice

almost

loop

charges

may

charged

temperature

the

of m a g n e t i c

term;

of

of magnetic c h a r g e s

produced after

filling

z there

equal

another is e q u a l

z k to t h e

the

tunnel

this

relations

link

to

at a higher

at n = O

formation and

the

(2) with

varJ.ous

state p=max

8=2~

b)

and At

numbers

with

confinement

temperature

the model

condensate

quantum

state

p>2J3;

topological

correspond

Bose

links;

gradient.

in 3

in 45

ground

invariance;

holes

one

term

low temperatures

diate

of

studied

8/21v a n d v a l u e s

loop

with

8

temperatures,the factors

lattice

diagram

of

the

account

version

account

8

the

circular

lattice

clockwise

effective on

anyon

the

6) t e r m w a s

dyna-

to t h e

2 depending

phase

without

statistical

spin

For a l o o p

the

The

on

Zk_{j is the d i s c r e t e

the

Let

e£fective hops

of

of t h e

developed

tile

neighbouring

exchange

because

Taking

hoppJ.ng c o h e r e n t l y to

a

an

the

with

of

loops.

of

or

v~l-v

of

of t h e

system

mics

an anyon

determined

A zk.5 z k-

gauge

to d e s c r i b e

of t h e

I

=

0=~ (p~q/2) . T h e

structure

ties

vortex

that

symmetry

choice

necessary

~ ( ~ + 2n)

v.

space the

changes

O~2~(p~q)

at

particle-hole

filling

means

are

the

when A=O

anyons

follows

This

q flux around

gauge,

of t w o

as

.~(~).

is a b o s o n

having

rotating

in

exp{i2,z/p}

17.

Nucl.

Phys.

205B

FS5