The Quantum Torus Chain

TL;DR

The paper introduces the quantum torus chain, a new class of 1D quantum lattice models with discrete symmetry and projective representations, exhibiting diverse phase behaviors depending on an integer parameter.

Contribution

It presents the quantum torus chain models, analyzing their phase structure and transitions, highlighting the role of the integer parameter in controlling frustration and phase types.

Findings

Models exhibit gapped symmetry breaking phases for even parameters.

Models show gapless phases separating gapped phases for odd parameters.

Analysis of phases and transitions for specific parameter values.

Abstract

We introduce a new set of one dimensional quantum lattice models which we refer to as The quantum torus chain. These models have discrete global symmetry, and projective on-site representations. They possess an integer-valued parameter which controls the presence or absence of frustration. Depending on whether this parameter is even or odd these models either exhibit gapped symmetry breaking phases with isolated critical points, or gapped symmetry breaking phases separated by gapless phases. We discuss the property of these phases and phase transitions for two special values of the parameter and point out many open problems