Chinese Physics Letters

Interfaces in the XY Model and Conformal Invariance

Degang Zhang, Zhong-jun Chen, Bo‐Zang Li

Published Jan 1, 1999• 5 citations

Abstract

The one-dimensional XY model with n arbitrarily placed interfaces is investigated. The energy spectrum is shown to have a tower structure only for a commensurate configuration of the critical parameters. The interfacial critical exponents in such cases are determined from conformal invariance theory. The underlying algebra generating the conformal spectrum is the shifted SO(4 c ) Kac-Moody algebra, the central charge is 2 c , which is exactly two times of that in the Ising model with the same structure of interfaces.

DOI: 10.1088/0256-307x/16/1/016

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Chinese Physics Letters

Interfaces in the XY Model and Conformal Invariance

Degang Zhang, Zhong-jun Chen, Bo‐Zang Li

Published Jan 1, 1999• 5 citations

Publisher

Abstract

DOI: 10.1088/0256-307x/16/1/016

Related papers

Interfaces in the Ising quantum chain and conformal invariance

Degang Zhang, Bo‐Zang Li, Min‐Guang Zhao

Physical review. B, Condensed matterApr 1, 19967 citations

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Bertrand Berche, Loïc Turban

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arXiv:cond-mat/9505048Physical review. B, Condensed matterSep 1, 199555 citations

Given a critical quantum spin chain with a microscopic Lie group symmetry, corresponding, e.g., to

U(1)

SU(2)

spin isotropy, we numerically investigate the emergence of Kac-Moody symmetry at low energies and long distances. In that regime, one such critical quantum spin chain is described by a conformal field theory where the usual Virasoro algebra associated with conformal invariance is augmented with a Kac-Moody algebra associated with conserved currents. Specifically, we first propose a method to construct lattice operators corresponding to the Kac-Moody generators. We then numerically show that, when projected onto low-energy states of the quantum spin chain, these operators indeed approximately fulfill the Kac-Moody algebra. The lattice version of the Kac-Moody generators allows us to compute the so-called level constant and to organize the low-energy eigenstates of the lattice Hamiltonian into Kac-Moody towers. We illustrate the proposal with the XXZ model and the Heisenberg model with a next-to-nearest-neighbor coupling.

{\mathit{Z}}_{2}

symmetries of which the fully frustrated XY model is a special case. The effective values obtained for c show a significant decrease with L at different points along the line where the transition to the ordered phase takes place in a single transition. Extrapolations based on power-law corrections give values consistent with c=3/2 although larger values cannot be ruled out. Critical exponents are obtained more accurately and are consistent with previous Monte Carlo simulations suggesting critical behavior and with recent calculations for the frustrated XY model.