Bulk-boundary correspondence for dynamical phase transitions in one-dimensional topological insulators and superconductors

Sedlmayr, Nicholas; Jaeger, P.; Maiti, Moitri; Sirker, Jesko

doi:10.1103/physrevb.97.064304

Cited by 71 publications

(58 citation statements)

References 31 publications

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“…Previously, a still not fully understood connection between the timescales of dynamical quantum phase transitions and dynamic entanglement entropy has been reported. 28 Oscillations in the dynamical entanglement entropy following a quench had a period exactly twice the critical timescale of the dynamical quantum phase transitions. The entanglement entropy is defined as a von-Neumann entropy for a subsystem after tracing out the rest of the system:…”

Section: Relation To the Dynamical Entanglement Entropymentioning

confidence: 99%

Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility

Masłowski¹,

Sedlmayr²

2020

Phys. Rev. B

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We investigate the Loschmidt amplitude and dynamical quantum phase transitions in multiband one dimensional topological insulators. For this purpose we introduce a new solvable multiband model based on the Su-Schrieffer-Heeger model, generalized to unit cells containing many atoms but with the same symmetry properties. Such models have a richer structure of dynamical quantum phase transitions than the simple two-band topological insulator models typically considered previously, with both quasiperiodic and aperiodic dynamical quantum phase transitions present. Moreover the aperiodic transitions can still occur for quenches within a single topological phase. We also investigate the boundary contributions from the presence of the topologically protected edge states of this model. Plateaus in the boundary return rate are related to the topology of the time evolving Hamiltonian, and hence to a dynamical bulk-boundary correspondence. We go on to consider the dynamics of the entanglement entropy generated after a quench, and its potential relation to the critical times of the dynamical quantum phase transitions. Finally, we investigate the fidelity susceptibility as an indicator of the topological phase transitions, and find a simple scaling law as a function of the number of bands of our multiband model which is found to be the same for both bulk and boundary fidelity susceptibilities. arXiv:1911.02831v3 [cond-mat.mes-hall] 1 Jan 2020

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Section: Relation To the Dynamical Entanglement Entropymentioning

confidence: 99%

Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility

Masłowski¹,

Sedlmayr²

2020

Phys. Rev. B

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“…A prominent example along these lines is provided by dynamical quantum phase transitions (DQPTs) [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], a counterpart of thermal phase transitions in coherent quantum time evolution, where the role of a control parameter is replaced by real time. The formal analog of a (boundary) partition function is in this context played by the Loschmidt amplitude…”

Section: Introductionmentioning

confidence: 99%

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

Mendl

Budich

2019

Phys. Rev. B

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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]

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“…In fact a direct comparison between the contribution of these two eigenvalues to the return rate and the boundary return rate shows remarkably good agreement. 16…”

Section: A Boundary Contributionsmentioning

confidence: 99%

“…(24) Alternatively one could consider averaging over the pure state Loschmidt amplitudes with a weighting determined by an initial density matrix: 36 Here we have used the metric generalisation for the Loschmidt echo |Lρ(t)|, see equation (23). 16 with S(t) being the time-evolution operator.…”

Section: Finite Temperaturesmentioning

confidence: 99%

Dynamical Phase Transitions in Topological Insulators

Sedlmayr

2019

Acta Phys. Pol. A

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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]

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Bulk-boundary correspondence for dynamical phase transitions in one-dimensional topological insulators and superconductors

Cited by 71 publications

References 31 publications

Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility

Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility

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

Dynamical Phase Transitions in Topological Insulators

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