Dynamical Phase Transitions in Topological Insulators

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.

Short lecture notes for the 13th International School on Theoretical Physics: Symmetry and Structural Properties of Condensed Matter, Rzeszów 10-15 September 2018. Some citations added to the second version

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Cited by in corpus (12)

• Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection
• Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility
• Many-body dynamical phase transition in quasi-periodic potential
• Liouvillian spectral collapse in the Scully-Lamb laser model
• Dynamical quantum phase transitions in a mesoscopic superconducting system
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Dynamical Quantum Phase Transitions Following Double Quenches: Persistence of the Initial State vs Dynamical Phases
• Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system
• Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter