Dynamical phase transitions and temporal orthogonality in one-dimensional hard-core bosons: from the continuum to the lattice

Abstract

We investigate the dynamics of the rate function and of local observables after a quench in models which exhibit phase transitions between a superfluid and an insulator in their ground states. Zeros of the return probability, corresponding to singularities of the rate functions, have been suggested to indicate the emergence of dynamical criticality and we address the question of whether such zeros can be tied to the dynamics of physically relevant observables and hence order parameters in the systems. For this we first numerically analyze the dynamics of a hard-core boson gas in a one-dimensional waveguide when a quenched lattice potential is commensurate with the particle density. Such a system can undergo a pinning transition to an insulating state and we find non-analytic behavior in the evolution of the rate function which is indicative of dynamical phase transitions. In addition, we perform simulations of the time dependence of the momentum distribution and compare the periodicity of this collapse and revival cycle to that of the non-analyticities in the rate function: the two are found to be closely related only for deep quenches. We then confirm this observation by analytic calculations on a closely related discrete model of hard-core bosons in the presence of a staggered potential and find expressions for the rate function for the quenches. By extraction of the zeros of the survival amplitude we uncover a non-equilibrium timescale for the emergence of non-analyticities and discuss its relationship with the dynamics of the experimentally relevant parity operator.

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

“…[32] and the lines of FZs were indeed found to cross the real time axis at those instants. This observation has been independently confirmed through several works on quenched one-dimensional (1D) integrable and non-integrable systems [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. Subsequent studies, however, have established that sudden quenching within the same phase of a system (both integrable and non-integrable) without ever encountering an equilibrium QCP may still give rise to DQPTs in some situations [54,55].…”

Critical slowing down and entanglement protection

“…tum critical behaviour are seen to persists at finite temperature [27,[29][30][31][32], and can be recognized in the behaviour of rather small Ising rings [33,34], meaning that the idea of exploiting critical features of the environment in designing apparatuses that embody quantum devices might be experimentally tested.…”

Dynamical Topological Quantum Phase Transitions in Nonintegrable Models

“…Namely, the obvious choice of an observable (e.g. the equilibrium order parameter) may not follow the dynamics dictated by the DQPTs and the connection between them remains elusive like in the case of a nonintegrable Ising chain [19] or Bose-Hubbard model [20]. Thus, the relation of DQPTs to observables in nonintegrable models deserves further investigation in general.In this work we study quenches starting from the Haldane phase to regimes where the ground state has trivial topology.…”