Spin and topological order in a periodically driven spin chain

TL;DR

This paper explores the rich topological phase diagram of a periodically driven quantum Ising chain, revealing multiple phases, phase transitions, and symmetry-breaking phenomena using Floquet theory.

Contribution

It systematically characterizes the Floquet ground state phases, including topological and symmetry-breaking phases, in a driven quantum spin chain, highlighting new phase transition behaviors.

Findings

Existence of infinitely many distinct Floquet phases.

Identification of second-order quantum phase transitions with order parameter changes.

Observation of Kibble-Zurek scaling during adiabatic phase transitions.

Abstract

The periodically driven quantum Ising chain has recently attracted a large attention in the context of Floquet engineering. In addition to the common paramagnet and ferromagnet, this driven model can give rise to new topological phases. In this work we systematically explore its quantum phase diagram, by examining the properties of its Floquet ground state. We specifically focus on driving protocols with time-reversal invariant points, and demonstrate the existence of an infinite number of distinct phases. These phases are separated by second-order quantum phase transitions, accompanied by continuous changes of local and string order parameters, as well as sudden changes of a topological winding number and of the number of protected edge states. When one of these phase transitions is adiabatically crossed, the correlator associated to the order parameter is nonvanishing over a length scale which shows a Kibble-Zurek scaling. In some phases, the Floquet ground state spontaneously breaks the discrete time-translation symmetry of the Hamiltonian. Our findings provide a better understanding of topological phases in periodically driven clean integrable models.