Dynamical detection of mean-field topological phases in an interacting Chern insulator

• URL: http://arxiv.org/abs/2206.11018v3
• Date: Fri, 12 Aug 2022 03:45:36 GMT
• Title: Dynamical detection of mean-field topological phases in an interacting Chern insulator
• Authors: Wei Jia, Long Zhang, Lin Zhang, Xiong-Jun Liu
• Abstract summary: We propose a scheme based on quench dynamics to detect the mean-field topological phase diagram of an insulator. We find two characteristic times $t_s$ and $t_c$ which capture the emergence of dynamical self-consistent particle number density. The number of mean-field topological phase is determined by the spin polarizations of four Dirac points at the time $t_s$.
• Score: 11.848843951626527
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Interactions generically have important effects on the topological quantum phases. For a quantum anomalous Hall (QAH) insulator, the presence of interactions can qualitatively change the topological phase diagram which, however, is typically hard to measure in the experiment. Here we propose a novel scheme based on quench dynamics to detect the mean-field topological phase diagram of an interacting Chern insulator, with nontrivial dynamical quantum physics being uncovered. We focus on a two-dimensional QAH system in the presence of a weak to intermediate Hubbard interaction which only drives a magnetic order under the mean-field level. After quenching the Zeeman coupling, both the mean-field Hamiltonian and many-body quantum state evolve over time. This is in sharp contrast to quenching a non-interacting system, in which only the many-body state evolves. We find two characteristic times $t_s$ and $t_c$ which capture the emergence of dynamical self-consistent particle number density and dynamical topological phase transition for the time-dependent Hamiltonian, respectively. An interesting result is that $t_s>t_c$ ($t_s<t_c$) occurs in repulsive (attractive) interaction when the system is quenched from an initial fully polarized state to the topologically nontrivial regimes, and $t_s=t_c$ characterizes the topological phase boundaries. Moreover, the topological number of mean-field topological phase is determined by the spin polarizations of four Dirac points at the time $t_s$. With these results we provide a feasible scheme to detect the mean-field topological phase diagram via the two characteristic times in quench dynamics, which can reveal the novel interacting effects on the topological phases and shall promote the experimental observation.

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