Floquet dynamical phase transition and entanglement spectrum

Abstract

We explore both pure and mixed states Floquet dynamical quantum phase transitions (FDQFTs) in the onedimensional p-wave superconductor with a time-driven pairing phase. In the Fourier space, the model is recast to the non-interacting quasi-spins subjected to a time-dependent effective magnetic field. We show that FDQFTs occur within a range of driving frequency without resorting to any quenches. Moreover, FDQFTs appear in the region where quasi-spins are in the resonance regime. In the resonance regime, the population completely cycles the population between the spin down and up states. Additionally, we study the conditions for the appearance of FDQFTs using the entanglement spectrum and purity entanglement measure. Our results imply that the entanglement spectrum can truly capture the resonance regime where FDQFTs occur. Particularly, the dynamical topological region results in the degeneracy of the entanglement spectrum. It is shown that the boundary of the driven frequency range, over which the system reveals FDQFTs, signaled by the purity entanglement measure.

Dynamics Reflect Gapless Edge Modes for Topological Superconductor

“…Besides quenching, Floquet dynamical quantum phase transition is another novel topic which has been explored for an extended XY model [39]. This kind of transition occurs within a range of driving frequency without resorting to quenches in 1-dimensional p-wave superconductor [40]. Different manners of changing parameters may reveal ample contents of dynamical phase transitions…”

Floquet dynamical quantum phase transitions in periodically quenched systems

“…Moreover, when the periodically driven system is initialized in a Floquet topological phase, the Floquet DQPTs would also show topologically nontrivial signatures, characterized by the quantized jump of a dynamical topological order parameter (DTOP) at each critical time of the transition [34]. In later studies, different aspects of Floquet DQPTs have * zhoulw13@u.nus.edu also been explored, such as the effects of mixed state and the properties of entanglement spectrum [48,49]. However, all the studies on Floquet DQPTs till now focus on a specific type of driving protocol, in which the system can be described by a static effective Hamiltonian in a rotating frame [34,48,49].…”

“…In later studies, different aspects of Floquet DQPTs have * zhoulw13@u.nus.edu also been explored, such as the effects of mixed state and the properties of entanglement spectrum [48,49]. However, all the studies on Floquet DQPTs till now focus on a specific type of driving protocol, in which the system can be described by a static effective Hamiltonian in a rotating frame [34,48,49]. Therefore, richer signatures of Floquet DQPTs under more general driving schemes have not been revealed.…”

Dynamical quantum phase transitions in a mesoscopic superconducting system

“…DQPTs manifest themselves by non-analytic (cusp-like) features appearing in the return rate function [4], in analogy to a static (classical or quantum) phase transitions revealing itself in the free energy at a critical temperature, magnetic field, pressure, etc. DQPTS have also been generalised to non ground state initial conditions with mixed results [5][6][7][8][9][10][11][12], and in driven systems [13][14][15][16][17][18][19][20][21]. So far, the studies of critical properties [22,23], dynamical order parameters [24,25], and spontaneously broken symmetries [26,27] have been mostly addressed in bulk systems, often in either spin chains [28][29][30][31][32][33][34] or topological insulators and superconductors [35][36][37][38][39][40][41][42][43][44].…”