Out-of-equilibrium density dynamics of a quenched fermionic system

Abstract

Using a Luttinger liquid theory we investigate the time evolution of the particle density of a one-dimensional fermionic system with open boundaries and subject to a finite duration quench of the inter-particle interaction. We provide analytical and asymptotic solutions to the unitary time evolution of the system, showing that both switching on and switching off the quench ramp create light-cone perturbations in the density. The post-quench dynamics is strongly affected by the interference between these two perturbations. In particular, we find that the discrepancy between the time-dependent density and the one obtained by a generalized Gibbs ensemble picture vanishes with an oscillatory behavior as a function of the quench duration, with local minima corresponding to a perfect overlap of the two light-cone perturbations. For adiabatic quenches, we also obtain a similar behavior in the approach of the generalized Gibbs ensemble density towards the one associated with the ground state of the final Hamiltonian.

Time evolution during and after finite-time quantum quenches in Luttinger liquids

“…However, we are not aware of quench protocols that allow for an exact, analytical solution of (52). The differential equation (52) and some properties of its solution will be further investigated in a separate work. 75 …”

“…Further aspects that were investigated include the excitation energy, the work statistics, finite-temperature initial states, the Loschmidt echo and the diagonal ensemble reached at late times. [46][47][48][49][50][51][52] In this article we aim at obtaining a complete understanding of finite-time quenches in Luttinger liquids. To this end we consider the time evolution during and after the quench and derive exact, analytical results to go beyond the perturbative regime.…”

Quench-induced entanglement and relaxation dynamics in Luttinger liquids

“…In recent years the LL model has also been proven to be a very powerful tool for studying the dynamics of 1D systems after a quench of the interaction strength. In particular, the subsequent relaxation towards a steady-state and the characterization of the latter has been the focus of many recent works [22,23,[43][44][45][46][47][48][49].…”

Finite-time quantum quenches in the XXZ Heisenberg chain

“…For the above mentioned Luttinger model this finitetime quench protocol has been studied in several works. 31,[34][35][36][37][38][39][40][41][42][43][44] In particular, the light-cone spreading in two-point correlation functions was found 35,42 to be delayed as compared to the light cone after sudden quenches, with the delay being related to the length and form of the finite-time quench protocol. Comparisons between the Luttinger model predictions and numerical simulations for interacting microscopic models have been limited so far, 31,35 with a detailed analysis of the lightcone spreading and aforementioned delay for the Heisenberg chain still missing.…”