Realization of higher Wess-Zumino-Witten models in spin chains

Building on the generalization of the exactly dimerized Majumdar-Ghosh ground state to arbitrary spin S for the Heisenberg chain with a three-site term (S_i1S_i)(S_iS_i+1)+H.c., we use density-matrix renormalization group simulations and exact diagonalizations to determine the nature of the dimerization transition for S=1, 3/2, and 2. The resulting central charge and critical exponent are in good agreement with the SU(2)_k=2S Wess-Zumino-Witten values c=3k/(2+k) and =3/(2+k). Since the three-site term that induces dimerization appears naturally if exchange interactions are calculated beyond second order, these results suggest that SU(2)_k>,1 Wess-Zumino-Witten models might finally be realized in actual spin chains.

75.10.Jm
75.10.Pq
75.40.Mg
spin: chain
density matrix: renormalization group
Wess-Zumino-Witten model
critical phenomena
central charge
ground state
Heisenberg

References(30)

Figures(0)

[1]

Zeitschrift fr Physik 71, 205 (1931)

H. Bethe

[2]

Absence of Mott transition in an exact solution of the short-range, one-band model in one dimension

Elliott H. Lieb
(
- Northeastern U.
)
,
F.Y. Wu
(
- Northeastern U.
)

- Phys.Rev.Lett. 20 (1968) 1445-1448,
- Phys.Rev.Lett. 21 (1968) 192 (erratum)
•
DOI:
- 10.1103/PhysRevLett.21.192.2

[3]

Solution of the Kondo Problem

N. Andrei
(
- Rutgers U., Piscataway
)
,
K. Furuya
(
- New York U.
)
,
J.H. Lowenstein
(
- New York U.
)

- Rev.Mod.Phys. 55 (1983) 331,
- Los Alamos Nonlin.1981:169
•
DOI:
- 10.1103/RevModPhys.55.331

[4]

Journal of Physics C:

P.B. Wiegmann

- Solid State Phys. 14 (1981) 1463

[5]

A General Model for Multicomponent Quantum Systems

Bill Sutherland
(
- SUNY, Stony Brook
)

- Phys.Rev.B 12 (1975) 3795-3805
•
DOI:
- 10.1103/PhysRevB.12.3795

[6]

The picture of low-lying excitations in the isotropic Heisenberg chain of arbitrary spins

L.A. Takhtajan
(
- Steklov Math. Inst., St. Petersburg
)

- Phys.Lett.A 87 (1982) 479-482
•
DOI:
- 10.1016/0375-9601(82)90764-2

[7]

EXACT SOLUTION OF THE ISOTROPIC HEISENBERG CHAIN WITH ARBITRARY SPINS: THERMODYNAMICS OF THE MODEL

Hratchya M. Babujian
(
- Moscow, ITEP
)

- Nucl.Phys.B 215 (1983) 317-336
•
DOI:
- 10.1016/0550-3213(83)90668-5

[8]

Critical Theory of Quantum Spin Chains

Ian Affleck
(
- Princeton U.
)
,
F.D.M. Haldane
(
- UC, San Diego
)

- Phys.Rev.B 36 (1987) 5291-5300
•
DOI:
- 10.1103/PhysRevB.36.5291

[9]

Journal of Physics A: Mathematical and General 21, L381 (1988)

F.C. Alcaraz
,
M.J. Martins

[10]

N. Andrei
,
H. Johannesson

- Phys.Lett.A 104 (1984) 370

[11]

The Structure of Low Lying Excitations in a New Integrable Quantum Chain Model

H. Johannesson
(
- Rutgers U., Piscataway
)

- Nucl.Phys.B 270 (1986) 235-272
•
DOI:
- 10.1016/0550-3213(86)90554-7

[12]

Generalized Parafermionic Theory and Integrable Ade Models

Marcio Jose Martins
(
- UC, Santa Barbara
)

- Phys.Rev.Lett. 65 (1990) 2091-2093,
- Phys. Rev. Lett. 65 (1990) 2091-2093 and Preprint - Martins, M.J. (90,rec.May) 8 p
•
DOI:
- 10.1103/PhysRevLett.65.2091