Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

Abstract

Dynamical quantum phase transitions (DQPTs) represent a counterpart in non-equilibrium quantum time evolution of thermal phase transitions at equilibrium, where real time becomes analogous to a control parameter such as temperature. In quenched quantum systems, recently the occurrence of DQPTs has been demonstrated, both with theory and experiment, to be intimately connected to changes of topological properties. Here, we contribute to broadening the systematic understanding of this relation between topology and DQPTs to multi-orbital and disordered systems. Specifically, we provide a detailed ergodicity analysis to derive criteria for DQPTs in all spatial dimensions, and construct basic counter-examples to the occurrence of DQPTs in multi-band topological insulator models. As a numerical case study illustrating our results, we report on microscopic simulations of the quench dynamics in the Harper-Hofstadter model. Furthermore, going gradually from multiband to disordered systems, we approach random disorder by increasing the (super) unit cell within which random perturbations are switched on adiabatically. This leads to an intriguing order of limits problem which we address by extensive numerical calculations on quenched one-dimensional topological insulators and superconductors with disorder. arXiv:1909.01402v1 [cond-mat.quant-gas]

Topology of critical chiral phases: multiband insulators and superconductors

“…Our work may open a path towards a more comprehensive study of symmetry protection of multiband topological phases at criticality, including those of nontranslational invariant models in higher dimensions and artificially generated phases from Floquet topological engineering 44 . The growing backdrop of relevant experimental systems [33][34][35][36][37][38][39] here holds up the prospect of some very interesting developments.…”

“…One should here recall that an enlarged unit cell implies that the spectrum of the model − be it a band insulator or a mean-field superconductor − displays a multiband structure in the Brillouin zone. Besides the possible relevance for experiments − including studies of multiband topological nanowires [33][34][35][36] , quasi-1D fermionic gases in synthetic gauge fields 37 , and 1D topological quantum phase transitions out of equilibrium 38,39 − an analysis of the multiband problem introduces several new facets which may advance our general understanding of topology at quantum criticality. One may here mention that the extended scenario presented in Ref.…”

Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators

“…We introduce DQPTs in two-band insulators according to Ref. 37, although they can be extended to multiband systems with one occupied band [39,49]. We consider a two-band model parameterized by a vector d(k) = (d x , d y , d z ).…”

“…Within a quantum quench, while a system is prepared as the ground state of an initial Hamiltonian, the state evolves under a different Hamiltonian with suddenly switched parameters. A dynamical quantum phase transition (DQPT) is also known as a nonequilibrium topological phenomenon induced by quantum quenches [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53].…”

Signatures of topology in quantum quench dynamics and their interrelation

“…These concepts characterize the post-quench time-evolution from quite different physical perspectives. For quench protocols within the same Altland-Zirnbauer (AZ) symmetry class [45][46][47], it is known that DQPTs appear as a consequence of crossing a quantum critical point between a trivial and a topological phase [36,37,39,48]. By contrast, ESCs are a quantum information signature generalizing the presence of protected boundary modes in the entanglement spectrum [49][50][51][52], thus representing an instantaneous property of the time-evolved state [34].…”