Quasiparticles as Detector of Topological Quantum Phase Transitions

TL;DR

This paper introduces a quasiparticle-based method to detect topological quantum phase transitions, applicable across various systems including fractals and quasicrystals, with low computational costs and broad applicability.

Contribution

It proposes a novel, boundary-condition independent approach using quasiparticle properties to identify topological phase transitions in diverse many-body systems.

Findings

Successfully applied to multiple examples, including complex systems beyond traditional probes.

Detected phase transitions with low numerical costs using simple quasiparticle charge properties.

Enabled analysis of larger systems and broader parameter ranges than previous methods.

Abstract

A number of tools have been developed to detect topological phase transitions in strongly correlated quantum systems. They apply under different conditions, but do not cover the full range of many-body models. It is hence desirable to further expand the toolbox. Here, we propose to use quasiparticle properties to detect quantum phase transitions. The approach is independent from the choice of boundary conditions, and it does not assume a particular lattice structure. The probe is hence suitable for, e.g., fractals and quasicrystals. The method requires that one can reliably create quasiparticles in the considered systems. In the simplest cases, this can be done by a pinning potential, while it is less straightforward in more complicated systems. We apply the method to several rather different examples, including one that cannot be handled by the commonly used probes, and in all the cases we find that the numerical costs are low. This is so, because a simple property, such as the charge of the anyons, is sufficient to detect the phase transition point. For some of the examples, this allows us to study larger systems and/or further parameter values compared to previous studies.