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Quasi-periodic dynamical phase transitions in multi-band topological insulators

Nicholas Sedlmayr

Bulletin of the American Physical SocietyMar 5, 20200 citations

Aperiodic dynamical quantum phase transition in multi-band Bloch Hamiltonian and its origin

Kaiyuan Cao, Hao Guo, Guangwen Yang

We investigate the dynamical quantum phase transition (DQPT) in the multi-band Bloch Hamiltonian of the one-dimensional periodic Kitaev model, focusing on quenches from a Bloch band. By analyzing the dynamical free energy and Pancharatnam geometric phase (PGP), we show that the critical times of DQPTs deviate from periodic spacing due to the multi-band effect, contrasting with results from two-band models. We propose a geometric interpretation to explain this non-uniform spacing. Additionally, we clarify the conditions needed for DQPT occurrence in the multi-band Bloch Hamiltonian, highlighting that a DQPT only arises when the quench from the Bloch states collapses the band gap at the critical point. Moreover, we establish that the dynamical topological order parameter, defined by the winding number of the PGP, is not quantized but still exhibits discontinuous jumps at DQPT critical times due to periodic modulation. Additionally, we extend our analysis to mixed-state DQPT and find its absence at non-zero temperatures.We investigate the dynamical quantum phase transition (DQPT) in the multi-band Bloch Hamiltonian of the one-dimensional periodic Kitaev model, focusing on quenches from a Bloch band. By analyzing the dynamical free energy and Pancharatnam geometric phase (PGP), we show that the critical times of DQPTs deviate from periodic spacing due to the multi-band effect, contrasting with results from two-band models. We propose a geometric interpretation to explain this non-uniform spacing. Additionally, we clarify the conditions needed for DQPT occurrence in the multi-band Bloch Hamiltonian, highlighting that a DQPT only arises when the quench from the Bloch states collapses the band gap at the critical point. Moreover, we establish that the dynamical topological order parameter, defined by the winding number of the PGP, is not quantized but still exhibits discontinuous jumps at DQPT critical times due to periodic modulation. Additionally, we extend our analysis to mixed-state DQPT and find its absence at non-zero temperatures.

arXiv:2303.15966Journal of Physics Condensed MatterJan 3, 20246 citations

Quantum phase transitions and order parameters of a topological insulator

Yanchao Li

Nano-Micro ConferenceJan 1, 20170 citations

Symmetry-protected quantum phase transition in topological insulators

L. -F. Liu, X. L. Zhang, Su-Peng Kou

The European Physical Journal BAug 1, 20121 citation

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

Tomasz Masłowski, Nicholas Sedlmayr

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.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:1911.02831Physical review. B./Physical review. BJan 6, 202041 citations

Topological Quantum Phase Transitions and Quench Dynamics

Shiuan-Fan Liou

Jan 1, 20190 citations

Aperiodic and quasi-periodic dynamical quantum phase transitions in multi-band topological insulators

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