Phase Transitions Between Topologically Distinct Gapped Phases in Isotropic Spin Ladders

TL;DR

This paper investigates topologically distinct gapped phases in two-leg spin ladder models, revealing that phase transitions occur when interpolating between different topological classes characterized by unique string orders.

Contribution

It demonstrates the existence of two topologically distinct classes of gapped phases with string order in spin ladders and analyzes the nature of phase transitions between them.

Findings

Gapped phases are divided into two topological classes.

String order characterizes each topological class.

Phase transitions occur when interpolating between different classes.

Abstract

We consider various two-leg ladder models exhibiting gapped phases. All of these phases have short-ranged valence bond ground states, and they all exhibit string order. However, we show that short-ranged valence bond ground states divide into two topologically distinct classes, and as a consequence, there exist two topologically distinct types of string order. Therefore, not all gapped phases belong to the same universality class. We show that phase transitions occur when we interpolate between models belonging to different topological classes, and we study the nature of these transitions.