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 nonanalyticities 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. arXiv:1910.02314v2 [cond-mat.mes-hall]

Many-body dynamical phase transition in quasi-periodic potential

“…DQPT has been investigated elaborately in various contexts of quantum phase transitions in quantum model systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], and also for topological transitions [19][20][21][22][23][24]. Along with sudden quench, periodically driven systems have been studied as well [25,26].…”

Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection

“…In the literature, several dynamical probes to the topological invariants of one-and twodimensional non-Hermitian phases have been proposed, such as the non-Hermitian extension of mean chiral displacements [39][40][41] and dynamical winding numbers [42][43][44][45]. In the meantime, DQPTs (i.e., nonanalytic behaviors of certain observables in time [47][48][49][50]) following a quench across the EPs of a non-Hermitian lattice model is investigated in [51], and the monotonic growth of a dynamical topological order parameter in time is observed if an isolated EP is crossed during the quench [51]. This discovery indicates an underlying relationship between the two notably different nonequilibrium phenomena, NHTPs and DQPTs.…”

Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system

“…On the other hand, various conditions have been identified under which a clear connection exists [17]. Rigorous examples are exactly solvable models that exhibit ground states with distinct topological invariants [22][23][24]. Here a quench across the phase boundaries always leads to DQPTs.…”