Cross-dimensional universality classes in static and periodically driven Kitaev models

TL;DR

This paper explores the phase diagram, criticality, and universality classes of static and periodically driven Kitaev models, revealing cross-dimensional universality and symmetry-controlled edge state chirality.

Contribution

It uncovers cross-dimensional universality classes in driven Kitaev models and demonstrates how periodic driving can engineer multiple critical behaviors and control edge state chirality.

Findings

Static Kitaev model criticality matches 1D Dirac universality

Driven Kitaev model exhibits additional 1D nodal loop criticality

Periodic driving enables control over Majorana edge state chirality

Abstract

The Kitaev model on the honeycomb lattice is a paradigmatic system known to host a wealth of nontrivial topological phases and Majorana edge modes. In the static case, the Majorana edge modes are nondispersive. When the system is periodically driven in time, such edge modes can disperse and become chiral. We obtain the full phase diagram of the driven model as a function of the coupling and the driving period. We characterize the quantum criticality of the different topological phase transitions in both the static and driven model via the notions of Majorana-Wannier state correlation functions and momentum-dependent fidelity susceptibilities. We show that the system hosts cross-dimensional universality classes: although the static Kitaev model is defined on a 2D honeycomb lattice, its criticality falls into the universality class of 1D linear Dirac models. For the periodically driven Kitaev model, besides the universality class of prototype 2D linear Dirac models, an additional 1D nodal loop type of criticality exists owing to emergent time-reversal and mirror symmetries, indicating the possibility of engineering multiple universality classes by periodic driving. The manipulation of time-reversal symmetry allows the periodic driving to control the chirality of the Majorana edge states.