Spatial Reflection and Associated String Order in Quantum Spin Chains

TL;DR

This paper explores how spatial reflection and nonlocal string order parameters reveal hidden symmetries and phase transitions in quantum spin chains, offering new tools for understanding and modeling these systems.

Contribution

It introduces a method to characterize nonlocal order via reflection-based string order parameters and develops an explicit scheme for symmetry detection in matrix product states.

Findings

String order parameters characterize various physical systems.

The scheme determines symmetry and string order in matrix product states.

Insights into the Haldane gap and quantum phase transitions.

Abstract

We investigate spatial reflection and associated nonlocal order in spin chain quantum systems. The proposed string order parameters, e.g., reflected via operations of the spatial reflection or combinations of it with spin reflection, are able to characterize a variety of physical systems and allow us to gain renewed insights to the statistical mechanism underlying phenomena such as the Haldane gap and quantum phase transitions. Besides revealing further the potential application of the generalized parity symmetry in numerical algorithm, we build an explicit scheme to determine the symmetry and the related string order for matrix product states so that one can construct ansatz models with presumed properties.