From sudden quench to adiabatic dynamics in the attractive Hubbard model

TL;DR

This paper investigates the transition from sudden to adiabatic dynamics in the attractive Hubbard model, revealing distinct regimes based on interaction strength and the role of initial state memory in non-equilibrium superconducting states.

Contribution

It characterizes the dynamical phase diagram during interaction ramps, identifying a sharp transition between weak and strong coupling regimes and their impact on system memory.

Findings

Weak coupling dynamics depend on energy injected.

Strong coupling dynamics retain initial state memory.

A sharp transition delineates different dynamical regimes.

Abstract

We study the crossover between the sudden quench limit and the adiabatic dynamics of superconducting states in the attractive Hubbard model. We focus on the dynamics induced by the change of the attractive interaction during a finite ramp time which is varied in order to track the evolution of the dynamical phase diagram from the sudden quench to the equilibrium limit. Two different dynamical regimes are realized for quenches towards weak and strong coupling interactions. At weak coupling the dynamics depends only on the energy injected into the system, whereas a dynamics retaining memory of the initial state takes place at strong coupling. We show that this is related to a sharp transition between a weak and a strong coupling quench dynamical regime, which defines the boundaries beyond which a dynamics independent from the initial state is recovered. Comparing the dynamics in the superconducting and non-superconducting phases we argue that this is due to the lack of an adiabatic connection to the equilibrium ground state for non-equilibrium superconducting states in the strong coupling quench regime.