Geometric Visualization of Dynamical Topological Phase Transitions in a Quenched Kitaev Model

Li-Na Luan, Shuai Liu, Zhi-Xu Zhang

S.R. Ghazanfari, Hosein Mokhtari

Leela Ganesh Chandra Lakkaraju, Sudip Kumar Haldar, Aditi Sen

An exactly solvable Kitaev model in a two-dimensional square lattice exhibits a topological quantum phase transition which is different from the symmetry-breaking transition at zero temperature. When the ground state of a nonlinearly perturbed Kitaev model with different strengths of perturbation taken as the initial state is quenched to a pure Kitaev model, we demonstrate that various features of the dynamical state, such as the Loschmidt echo and time-averaged multipartite entanglement, can determine whether the initial state belongs to the topological phase or not. Moreover, the derivatives of the dynamical quantifiers can faithfully identify the topological quantum phase transition, which is present at equilibrium. When the individual qubits of the lattice interact with the local thermal bath repeatedly, we observe that block entanglement in dissipative dynamics can, nevertheless, distinguish the equilibrium phases from which the system starts evolution.

Guang-Ming Zhang

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.

Qi Chen, Guo-Qing Zhang, Jun-Qing Cheng +1 more