Quantization of topological indices in critical chains at low temperatures

TL;DR

This paper extends topological indices to finite temperatures in critical chains, demonstrating their quantization at low temperatures and analyzing their robustness to disorder through analytical and numerical methods.

Contribution

It introduces a formalism for quantizing topological indices at finite temperatures and applies it to critical chains, bridging gapped and gapless systems.

Findings

Topological indices are quantized at low temperatures in critical chains.

The formalism is validated analytically and numerically on chiral critical chains.

Topological indices show robustness against certain disorder perturbations.

Abstract

Various types of topological phenomena at criticality are currently under active research. In this paper we suggest to generalize the known topological quantities to finite temperatures, allowing us to consider gapped and critical (gapless) systems on the same footing. It is then discussed that the quantization of the topological indices, also at critically, is retrieved by taking the low-temperature limit. This idea is explicitly illustrated on a simple case study of chiral critical chains where the quantization is shown analytically and verified numerically. The formalism is also applied for studying robustness of the topological indices to various types of disordering perturbations.