The modified XXZ Heisenberg chain, conformal invariance, surface exponents of c<1 systems, and hidden symmetries of the finite chains

TL;DR

This paper investigates the spectral properties of the modified XXZ Heisenberg chain with boundary terms, revealing unexpected degeneracies linked to Virasoro algebra representations in systems with central charge less than one.

Contribution

It demonstrates how specific boundary conditions induce degeneracies connected to hidden symmetries and conformal invariance in the XXZ chain for c<1.

Findings

Spectral degeneracies occur at certain parameter tunings.

Degeneracies relate to Virasoro algebra representations.

Boundary terms influence the conformal structure.

Abstract

The spin-1/2 XXZ Heisenberg chain with two types of boundary terms is considered. For the first type, the Hamiltonian is hermitian but not for the second type which includes the U_{q}[SU(2)] symmetric case. It is shown that for a certain `tuning' between the anisotropy angle and the boundary terms the spectra present unexpected degeneracies. These degeneracies are related to the structure of the irreducible representations of the Virasoro algebras for c<1.