Dynamical Phase Transitions in Topological Insulators

TL;DR

This paper explores the concept of dynamical phase transitions in topological insulators, highlighting their role in understanding topological phases, edge states, and effects of non-equilibrium conditions.

Contribution

It provides an overview of how dynamical phase transitions relate to topological insulators and examines their implications for edge states and non-equilibrium scenarios.

Findings

Dynamical phase transitions can reveal topological properties.

Topologically protected edge states influence dynamical phase transitions.

Environmental effects modify the dynamical behavior of topological systems.

Abstract

The traditional concept of phase transitions has, in recent years, been widened in a number of interesting ways. The concept of a topological phase transition separating phases with a different ground state topology, rather than phases of different symmetries, has become a large widely studied field in its own right. Additionally an analogy between phase transitions, described by non-analyticities in the derivatives of the free energy, and non-analyticities which occur in dynamically evolving correlation functions has been drawn. These are called dynamical phase transitions and one is often now far from the equilibrium situation. In these short lecture notes we will give a brief overview of the history of these concepts, focusing in particular on the way in which dynamical phase transitions themselves can be used to shed light on topological phase transitions and topological phases. We will go on to focus, first, on the effect which the topologically protected edge states, which are one of the interesting consequences of topological phases, have on dynamical phase transitions. Second we will consider what happens in the experimentally relevant situations where the system begins either in a thermal state rather than the ground state, or exchanges particles with an external environment.