Out-of-equilibrium phase diagram of long-range superconductors

Abstract

Within the ultimate goal of classifying universality in quantum many-body dynamics, understanding the relation between out-of-equilibrium and equilibrium criticality is a crucial objective. Models with power-law interactions exhibit rich well-understood critical behavior in equilibrium, but the out-of-equilibrium picture has remained incomplete, despite recent experimental progress. We construct the rich dynamical phase diagram of free-fermionic chains with power-law hopping and pairing and provide analytic and numerical evidence showing a direct connection between nonanalyticities of the return rate and zero crossings of the string order parameter. Our results may explain the experimental observation of so-called accidental dynamical vortices, which appear for quenches within the same topological phase of the Haldane model, as reported by Fläschner et al. [Nat. Phys. 14, 265 (2018)]. Our work is readily applicable to modern ultracold-atom experiments, not least because state-of-the-art quantum gas microscopes can now reliably measure the string order parameter, which, as we show, can serve as an indicator of dynamical criticality.

Hybrid infinite time-evolving block decimation algorithm for long-range multidimensional quantum many-body systems

“…[80] and proven analytically in Refs. [81,84], the presence of local excitations as the lowestlying quasiparticles of the quench Hamiltonian is a necessary condition for anomalous cusps to arise. Hence, this clearly establishes that we are effectively working in 2D based on the equilibrium and dynamical characteristics of this model.…”

Dynamical quantum phase transitions in the one-dimensional extended Fermi-Hubbard model

“…Extending this idea to the nonequilibrium realm, a DQPT at a critical time t * (instead of a critical control parameter) is said to occur when during the dynamics, such zeros are crossed [15]. A vast amount of recent theoretical research has been devoted to study this beautiful insight in systems of different nature, namely spin [15,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], fermionic [33][34][35][36][37], bosonic [38][39][40][41][42][43], and hybrid models [44]. This effort also includes the analysis of the impact of ingredients such as disorder [45,46] and topological order [47,48].…”

Out-of-time-order correlations and Floquet dynamical quantum phase transition

“…Recently, a new research area of quantum phase transition has been investigated in nonequilibrium quantum systems, called dynamical quantum phase transitions (DQPTs) as a counterpart of equilibrium thermal phase transitions [75,76]. DQPT represents a phase transitions between dynamically emerging quantum phases, that occurs during the nonequilibrium coherent quantum time evolution under quenching [76][77][78][79][80] or time-periodic modulation of Hamiltonian [81][82][83][84][85][86][87]. In DQPT the real time acts as a control parameter analogous to temperature in conventional equilibrium phase transitions.…”