Spectrum of a duality-twisted Ising quantum chain

TL;DR

This paper analyzes the energy spectrum and conformal properties of an Ising quantum chain with a duality-twisted boundary condition, revealing new insights into its symmetry and boundary effects at criticality.

Contribution

It provides an analytical calculation of the complete energy spectrum for finite systems with duality-twisted boundary conditions and explores their conformal properties at criticality.

Findings

Complete energy spectrum derived analytically.

Identification of conformal twisted boundary condition.

Explicit form of the generalized twisted partition function.

Abstract

The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which becomes a symmetry of the model at the critical point. Thus, at the critical point, the Ising quantum chain with the duality-twisted boundary is translationally invariant, similar as in the case of the usual periodic or antiperiodic boundary conditions. The complete energy spectrum of the Ising quantum chain is calculated analytically for finite systems, and the conformal properties of the scaling limit are investigated. This provides an explicit example of a conformal twisted boundary condition and a corresponding generalised twisted partition function.