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

Balázs Pozsgay, Viktor Eisler

Research output: Contribution to journalArticle

Abstract

We study the time evolution of an integrable many-particle system, described by the q-boson Hamiltonian in the limit of strong bosonic interactions q→. 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.

Original languageEnglish
Article number053107
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2016
Issue number5
DOIs
Publication statusPublished - 19 May 2016

Keywords

  • integrable spin chains (vertex models)
  • quantum integrability (Bethe Ansatz)
  • quantum quenches
  • solvable lattice models

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistical and Nonlinear Physics
  • Statistics, Probability and Uncertainty

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