Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model

Abstract

We study the behavior of Fisher Zeros (FZs) and dynamical quantum phase transitions (DQPTs) for a linearly ramped Haldane model occurring in the subsequent temporal evolution of the same and probe the intimate connection with the equilibrium topology of the model. Here, we investigate the temporal evolution of the final state of the Haldane Hamiltonian (evolving with time-independent final Hamiltonian) reached following a linear ramping of the staggered (Semenoff) mass term from an initial to a final value, first selecting a specific protocol, so chosen that the system is ramped from one non-topological phase to the other through a topological phase. We establish the existence of three possible behaviour of areas of FZs corresponding to a given sector: (i) no-DQPT, (ii) one-DQPT (intermediate) and (iii)two-DQPTs (re-entrant), depending on the inverse quenching rate τ . Our study also reveals that the appearance of the areas of FZs is an artefact of the nonzero (quasi-momentum dependent) Haldane mass (MH ), whose absence leads to an emergent onedimensional behaviour indicated by the shrinking of the areas FZs to lines and the non-analyticity in the dynamical "free energy" itself. Moreover, the characteristic rates of crossover between the three behaviour of FZs are determined by the time-reversal invariant quasi-momentum points of the Brillouin zone where MH vanishes. Thus, we observe that through the presence or absence of MH , there exists an intimate relation to the topological properties of the equilibrium model even when the ramp drives the system far away from equilibrium.

Floquet dynamical quantum phase transitions

“…Experimentally, DQPTs have been observed in trapped ions [3,10], cold atoms [11,12], superconducting qubits [13], nanomechanical oscillators [14], and photonic quantum walks [15,16].To date, in most studies of DQPTs, a quantum quench acts as a trigger for initiating nonequilibrium dynamics and then exposing the underlying topological features. However, DQPTs under more general nonequilibrium manipulations are still largely unexplored [17][18][19]. In particular, because the dynamics of systems under time-periodic modulations has led to fascinating discoveries like Floquet topological states [20-24] and discrete time crystals [25][26][27], it is urgent to investigate how DQPTs may occur in such Floquet systems.…”

Dynamical quantum phase transitions in non-Hermitian lattices

“…As a promising framework to classify quantum dynamics of nonequilibrium many-body systems, DQPTs have been studied intensively in recent years [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The generality and topological feature of DQPTs were demonstrated in both lattice and continuum systems [20], across different spatial dimensions [21][22][23][24][25], and under various dynamical protocols [26][27][28]. The defining features of DQPTs have also been observed in recent experiments [29][30][31].Following the initial proposal, most studies on DQPTs focus on closed quantum systems undergoing unitary time evolution.…”

Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices

“…Loschmidt echo is a powerful method for analyzing nonequilibrium dynamics [95][96][97][98][99][100][101][102][103][104][105][106][107][108][109][110][111], which can exhibit a series of zero points if the initial and the post-quench systems are located in different phases at some time intervals. Up to now, it has been successfully applied in a series of models, such as transverse field Ising model [95], XY model [104,105], topological models [103, 106-108], Hubbard and Falicov-Kimball models [97] and disorder models [109].…”