Constructing Landau framework for topological order: Quantum chains and ladders

TL;DR

This paper develops a Landau framework to analyze topological order and hidden symmetries in quantum spin chains and ladders, enabling analytical study of phase transitions and topological properties.

Contribution

It introduces a unified analytical approach to topological order in spin models using mappings to fermionic systems and duality transformations within the Landau paradigm.

Findings

Calculated phase diagrams and boundaries for spin chains and ladders

Identified topological phases using Pontryagin (winding) numbers

Provided a comprehensive Landau description of quantum criticality

Abstract

We studied quantum phase transitions in the antiferromagnetic dimerized spin-1/2 XY chain andvtwo-leg ladders. From analysis of several spin models we present our main result: the framework to deal with topological orders and hidden symmetries within the Landau paradigm. After mapping of the spin Hamiltonians onto the tight-binding models with Dirac or Majorana fermions and, when necessary, the mean-field approximation, the analysis can be done analytically. By utilizing duality transformations the calculation of nonlocal string order parameters is mapped onto the local order problem in some dual representation and done without further approximations. Calculated phase diagrams, phase boundaries, order parameters and their symmetries for each of the phases provide a comprehensive quantitative Landau description of the quantum critical properties of the models considered. Complementarily, the phases with hidden orders can also be distinguished by the Pontryagin (winding) numbers which we have calculated as well. This unified framework can be straightforwardly applied for various spin chains and ladders, topological insulators and superconductors. Applications to other systems are under way.