Fidelity and Entropy Production in Quench Dynamics of Interacting Bosons in an Optical Lattice

Camille Lévêque,Barnali Chakrabarti,Axel U J Lode,Rhombik Roy,Arnaldo Gammal

doi:10.3390/quantum1020028

Abstract

We investigate the dynamics of a few bosons in an optical lattice induced by a quantum quench of a parameter of the many-body Hamiltonian. The evolution of the many-body wave function is obtained by solving the time-dependent many-body Schrödinger equation numerically, using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We report the time evolution of three key quantities, namely, the occupations of the natural orbitals, that is, the eigenvalues of the one-body reduced density matrix, the many-body Shannon information entropy, and the quantum fidelity for a wide range of interactions. Our key motivation is to characterize relaxation processes where various observables of an isolated and interacting quantum many-body system dynamically converge to equilibrium values via the quantum fidelity and via the production of many-body entropy. The interaction, as a parameter, can induce a phase transition in the ground state of the system from a superfluid (SF) state to a Mott-insulator (MI) state. We show that, for a quench to a weak interaction, the fidelity remains close to unity and the entropy exhibits oscillations. Whereas for a quench to strong interactions (SF to MI transition), the relaxation process is characterized by the first collapse of the quantum fidelity and entropy saturation to an equilibrium value. The dip and the non-analytic nature of quantum fidelity is a hallmark of dynamical quantum phase transitions. We quantify the characteristic time at which the quantum fidelity collapses and the entropy saturates.

Highlights

The non-equilibrium dynamical properties and statistical relaxation, where various observables of an isolated and interacting quantum many-body system dynamically converge to equilibrium values, have garnered immense interest in the last decade [1,2,3,4]
It is an established fact that an isolated quantum system thermalizes; the eigenstate thermalization hypothesis (ETH) states that the thermalization of an isolated quantum system is approached when the expectation values of observables relax to an equilibrium and approach their long-time average value given by the Gibbs ensemble [8,9,10]
We investigate the dynamics of the system following a quantum quench

Summary

Introduction

The non-equilibrium dynamical properties and statistical relaxation, where various observables of an isolated and interacting quantum many-body system dynamically converge to equilibrium values, have garnered immense interest in the last decade [1,2,3,4]. It is an established fact that an isolated quantum system thermalizes; the eigenstate thermalization hypothesis (ETH) states that the thermalization of an isolated quantum system is approached when the expectation values of (few-body) observables relax to an equilibrium and approach their long-time average value given by the Gibbs ensemble [8,9,10]. The analysis of the time-evolution of an isolated quantum many-body system far from equilibrium is the most fundamental way to establish its thermalization. In some recent works [14,15], one-dimensional spin−

Methods

Results

Conclusion