Detection of gapped phases of a 1D spin chain with onsite and spatial symmetries

TL;DR

This paper explores the phase diagram of a quantum spin-1 chain with onsite and spatial symmetries, identifying various gapped phases, phase transitions, and the interplay of symmetry-breaking and fractionalization.

Contribution

It introduces a comprehensive analysis of gapped phases in a spin chain with combined onsite and spatial symmetries using matrix product state order parameters.

Findings

Identification of multiple gapped phases with SPT order and symmetry breaking

Observation of continuous phase transitions between topologically nontrivial phases

Analysis of the interplay between onsite and spatial symmetries

Abstract

We investigate the phase diagram of a quantum spin-1 chain whose Hamiltonian is invariant under a global onsite $A_4$, translation and lattice inversion symmetries. We detect different gapped phases characterized by SPT order and symmetry breaking using matrix product state order parameters. We observe a rich variety of phases of matter characterized by a combination of symmetry breaking and symmetry fractionalization and also the interplay between the onsite and spatial symmetries. Examples of continuous phase transitions directly between topologically nontrivial SPT phases are also observed.