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

Abstract

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

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.…”

“…Eq. (39), into the prescription H j,j+n = (1 2)Ψ † H j,j+n Ψ, we find that only four of them, corresponding to (a), (b), (g), and (h), give a nonzero second-quantized Hamiltonian. In the other four cases, the hermiticity of H j,j+n when combined with the fermion algebra cancels out the resulting second-quantized expressions, signaling an incompatibility with fermion statistics.…”

“…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.…”

Genuine tripartite entanglement as a probe of quantum phase transitions in a spin-1 Heisenberg chain with single-ion anisotropy

“…This particular property of the ground-state fidelity makes it possible to identify topological phase transitions in many-body systems. Besides the ground-state fidelity and the fidelity susceptibility, there are other approaches to characterize topolog-ical phase transitions, such as the entanglement entropy in the ground-state of many-body systems [13][14][15][16], and the quantum discord of the ground state which is the difference between the quantum analogues of two classically equivalent expressions of mutual information [17][18][19][20][21].…”

Linear mapping between magnetic susceptibility and entanglement in conventional and exotic one-dimensional superfluids

“…Entanglement, which is a theoretical concept from quantum information theory, has attracted attention from nanoscience and nanotechnology since it is considered a fundamental resource for quantum computation 1,2 and quantum-enhanced metrology 3 . Entanglement has also played a central role in bridging quantum information theory to different areas, as condensed-matter, high-energy and cold-atoms physics [4][5][6][7][8][9][10][11][12][13][14][15][16][17] . By investigating entanglement properties one can probe quantum phase transitions [18][19][20][21][22][23] and characterise quantum many-body states, including exotic states of matter as Fulde-Ferrel-Larkin-Ovchnnikov superfluidity (FFLO) [24][25][26][27][28][29][30] , many-body localization 31,32 and topological spin liquids 33 .…”