Real-time dynamics in a strongly interacting bosonic hopping model: Global quenches and mapping to the XX chain

TL;DR

This paper analyzes the real-time dynamics of a strongly interacting bosonic model, providing exact formulas for key observables, mapping to the XX chain, and confirming the Generalized Gibbs Ensemble predictions.

Contribution

It introduces a non-local mapping of the $q$-boson model to the XX chain and derives exact, computationally efficient formulas for dynamical observables.

Findings

Exact formulas for Loschmidt-echo and emptiness formation probability

Mapping of the $q$-boson model to the XX spin chain

Verification of the Generalized Gibbs Ensemble in the large volume limit

Abstract

We study the time evolution of an integrable many-particle system, described by the $q$-boson Hamiltonian in the limit of strong interactions $q\to\infty$. It is shown that, for a particular class of pure initial states, the analytical calculation of certain observables simplifies considerably. Namely, we provide exact formulas for the calculation of the Loschmidt-echo and the emptiness formation probability, where the computational time scales polynomially with the particle number. Moreover, we construct a non-local mapping of the $q$-boson model to the XX spin chain, and show how this can be utilized to obtain the time evolution of various local bosonic observables for translationally invariant initial states. The results obtained via the bosonic and fermionic picture show perfect agreement. In the infinite volume and large time limits, we rigorously verify the prediction of the Generalized Gibbs Ensemble for homogeneous initial Fock states.