Self-dual $S_3$-invariant quantum chains

TL;DR

This paper explores the phase diagram of a self-dual three-state quantum chain with various symmetries, revealing complex phases including critical points, coexistence phases, and emergent supersymmetry, with connections to conformal field theories.

Contribution

It provides a detailed analysis of the phase structure of the self-dual $S_3$-invariant quantum chain, identifying new critical phases and emergent symmetries not previously characterized.

Findings

Identification of gapped phases with order-disorder coexistence

Discovery of integrable critical points with U(1) symmetry

Observation of an unusual critical phase combining two conformal field theories

Abstract

We investigate the self-dual three-state quantum chain with nearest-neighbor interactions and $S_3$, time-reversal, and parity symmetries. We find a rich phase diagram including gapped phases with order-disorder coexistence, integrable critical points with U(1) symmetry, and ferromagnetic and antiferromagnetic critical regions described by three-state Potts and free-boson conformal field theories respectively. We also find an unusual critical phase which appears to be described by combining two conformal field theories with distinct "Fermi velocities". The order-disorder coexistence phase has an emergent fractional supersymmetry, and we find lattice analogs of its generators.