Metal--topological-insulator transition in the quantum kicked rotator with Z2 symmetry

TL;DR

This paper extends the quantum kicked rotator model to include topological insulator phases, demonstrating a metal-topological insulator transition with disorder-insensitive critical exponents, using a scattering approach and incommensurate driving frequencies.

Contribution

It introduces a new topological phase transition framework within the quantum kicked rotator model, incorporating Z2 invariants and disorder effects.

Findings

The critical exponent is independent of the topological invariant.

The model effectively captures metal-topological insulator transitions.

Scaling laws are studied using incommensurate driving frequencies.

Abstract

The quantum kicked rotator is a periodically driven dynamical system with a metal-insulator transition. We extend the model so that it includes phase transitions between a metal and a topological insulator, in the universality class of the quantum spin Hall effect. We calculate the Z2 topological invariant using a scattering formulation that remains valid in the presence of disorder. The scaling laws at the phase transition can be studied efficiently by replacing one of the two spatial dimensions with a second incommensurate driving frequency. We find that the critical exponent does not depend on the topological invariant, in agreement with earlier independent results from the network model of the quantum spin Hall effect.