Quantum quench dynamics in topological systems

Haiping Hu, Erhai Zhao

Graham Kells, Diptiman Sen, Johannes K. Slingerland +1 more

Lorenzo Pastori, Simone Barbarino, Jan Carl Budich

This paper studies the topological properties in the time evolution of a system after a quantum quench, by comparing the different signatures that can be used to detect topological properties in the out-of-equilibrium dynamics.

Ryo Okugawa, Hiroki Oshiyama, Masayuki Ohzeki

Dynamical quantum phase transitions (DQPTs) are topologically characterized in quantum quench dynamics in topological systems. In this paper, we study Loschmidt amplitudes and DQPTs in quantum quenches in mirror-symmetric topological phases. Based on the topological classification of mirror-symmetric insulators, we show that mirror symmetry creates symmetry-protected DQPTs. If mirror symmetry is present, topologically robust DQPTs can occur in quantum quenches, even in high-dimensional time-reversal invariant systems. Then, we also show that symmetry-protected DQPTs occur in quenches in two-dimensional chiral-symmetric systems with mirror symmetry. Mirror-symmetry-protected DQPTs can be easily captured by a reduced rate function. Moreover, we introduce dynamical topological order parameters for mirror-symmetry-protected DQPTs. Finally, we demonstrate DQPTs using lattice models for a time-reversal invariant topological crystalline insulator and a higher-order topological insulator.

Shiuan-Fan Liou

Tian-Shu Deng, Wei Yi

In this review, we discuss the recent progress on the study of dynamic topological phenomena in quench dynamics. In particular, we focus on dynamic quantum phase transition and dynamic topological invariant, both of which are hinged upon the existence of fixed points in the dynamics. Further, the existence of these fixed points are topologically protected, in the sense that their existence are closely related to static topological invariants of pre- and post-quench Hamiltonians. We also discuss under what condition these dynamic topological phenomena are robust in non-unitary quench dynamics governed by non-Hermitian Hamiltonians. So far, dynamic topological phenomena have been experimentally observed in synthetic systems such as cold atomic gases, superconducting qubits, and linear optics. These studies extend our understanding of topological matter to the non-equilibrium regime.