Dynamical Quantum Phase transitions and Recurrences in the Non-Equilibrium BCS model

Abstract

Non-equilibrium aspects of the BCS model have fascinated physicists for decades, from the seminal works of Eliashberg to modern realizations in cold atom experiments. The latter scenarios have lead to a great deal of interest in the quench dynamics of fermions with pairing interactions. The recently introduced notion of a dynamical quantum phase transition is an attempt to classify the myriad of possible phenomena which can result in such far from equilibrium systems. These are defined as non-analytic points of the logarithm of the Loschmidt echo and are linked to oscillations in the dynamics a systems order parameter. In this work we analytically investigate the relation between DQPTs and oscillation of the superconducting order parameter in quenches of the BCS model. We find that each oscillation of the order parameter is accompanied by a DQPT which is first order in nature. We show this for a variety of initial states and furthermore find that when the order parameter attains a constant steady state then no DQPTS occur.

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].…”

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][33], fermionic [34][35][36][37][38][39], bosonic [40][41][42][43][44][45], and hybrid models [46]. This effort also includes the analysis of the impact of ingredients such as disorder [47][48][49] and topological order [50][51][52].…”

Entanglement view of dynamical quantum phase transitions

“…In order to connect DQPTs to equilibrium concepts, such as order parameters, the behavior of local observables was explored [22,26,34]. A direct correspondence was established for systems with broken symmetries, involving a generalized notion of DQPTs [11,17,20,35]; however, the relation between DQPTs and local expec-tation values in general situations remains elusive.…”