Souvik Bandyopadhyay — Page 2

arXiv2019

Temporal variation in the winding number due to dynamical symmetry breaking and associated transport in a driven SSH chain

Considering a BDI symmetric one-dimensional SSH model, we explore the fate of the bulk topological invariant, namely, the winding number under a generic time dependent perturbation; the effective Hamiltonian, that generates the temporal evolution of the initial (ground) state of the completely symmetric initial Hamiltonian, may have the same or different symmetries. To exemplify, we consider the following protocols, namely (i) a perfectly periodic protocol (ii) a periodic protocol with noisy perturbations and also (iii) sudden changes in the parameters of the initial Hamiltonian. We establish that the topological invariant may change in some cases when the effective Hamiltonian (or the Floquet Hamiltonian in the periodic situation when observed stroboscopically) does not respect all BDI symmetries; this is manifested in the associated particle (polarisation) or heat current in the bulk. Our results establish a strong connection between the time evolution of the winding number (thus, the associated transport of currents) and the symmetry of the Hamiltonian generating the time evolution which has been illustrated considering an exhaustive set of possibilities.

cond-mat.stat-mech↗

arXiv2018

Exploring the possibilities of dynamical quantum phase transitions in the presence of a Markovian bath

We explore the possibility of dynamical quantum phase transitions (DQPTs) occurring during the temporal evolution of a quenched transverse field Ising chain coupled to a particle loss type of bath (local in Jordan-Wigner fermion space) using two versions of the Loschmidt overlap (LO), namely, the fidelity induced LO and the interferometric phase induced LO. The bath, on the one hand, dictates the dissipative evolution following a sudden quench and on the other, plays a role in dissipative mixed state preparation in the later part of the study. During a dissipative evolution following a sudden quench, no trace of DQPTs are revealed in both the fidelity and the interferometric phase approaches; however, remarkably the interferometric phase approach reveals the possibility of inter-steady state DQPTs in passage from one steady state to the other when the system is subjected to a quench after having reached the first steady state. We further probe the occurrences of DQPTs when the system evolves unitarily after being prepared in a mixed state of engineered purity by ramping the transverse field in a linear fashion in the presence of the bath. In this case though the fidelity approach fails to indicate any DQPT, the interferometric approach indeed unravels the possibility of occurrence of DQPTs which persists even up to a considerable loss of purity of the engineered initial state as long as a constraint relation involving the dissipative coupling and ramping time (rate) is satisfied. This constraint relation also marks the boundary between two dynamically inequivalent phases; in one the LO vanishes for the critical momentum mode (and hence DQPTs exist) while in the other no such critical mode can exist and hence the LO never vanishes.

cond-mat.stat-mech↗