Universal quantum criticality in static and Floquet-Majorana chains

TL;DR

This paper investigates universal quantum criticality in static and Floquet Majorana chains using a renormalization group approach, revealing common critical behavior and unique features in driven systems.

Contribution

It introduces a unified RG framework to analyze topological phase transitions in static and Floquet Kitaev chains, highlighting universal critical properties.

Findings

Identifies topological phase boundaries via divergences in Berry connections.

Proposes a correlation function and decay length as indicators of quantum criticality.

Discovers unique RG flow features related to non-high symmetry point gap closures in Floquet systems.

Abstract

The topological phase transitions in static and periodically driven Kitaev chains are investigated by means of a renormalization group (RG) approach. These transitions, across which the numbers of static or Floquet Majorana edge modes change, are accompanied by divergences of the relevant Berry connections. These divergences at certain high symmetry points in momentum space form the basis of the RG approach, through which topological phase boundaries are identified as a function of system parameters. We also introduce several aspects to characterize the quantum criticality of the topological phase transitions in both static and Floquet systems: a correlation function that measures the overlap of Majorana-Wannier functions, the decay length of the Majorana edge mode and a scaling law relating the critical exponents. These indicate a common universal critical behavior for topological phase transitions, in both static and periodically driven chains. For the latter, the RG flows additionally display intriguing features related to gap closures at non-high symmetry points due to momentarily frozen dynamics.