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arXiv:2006.16088 · Physical Review Research

Large-scale thermalization, prethermalization, and impact of temperature in the quench dynamics of two unequal Luttinger liquids

Paola Ruggiero, Laura Foini, Thierry Giamarchi

Published Jan 14, 2021• 28 citations
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Abstract

The work studies the dynamics following a quench in the tunneling between two different interacting Bose gases which are initially coupled. The authors highlight the quasi-thermal behaviour occurring at large times in the large distance regime, and its limit of validity.
DOI
10.1103/physrevresearch.3.013048

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We study the Bose-Hubbard and Fermi-Hubbard models in the (formal) limit of large coordination numbers $Z\ensuremath{\gg}1$. Via an expansion into powers of 1/Z1/Z1/Z, we establish a hierarchy of correlations which facilitates an approximate analytical derivation of the time evolution of the reduced density matrices for one and two sites, etc. With this method, we study the quantum dynamics (starting in the ground state) after a quantum quench, i.e., after suddenly switching the tunneling rate JJJ from zero to a finite value, which is still in the Mott regime. We find that the reduced density matrices approach a (quasi)equilibrium state after some time. For one lattice site, this state can be described by a thermal state (within the accuracy of our approximation). However, the (quasi)equilibrium state of the reduced density matrices for two sites including the correlations can not be described by a thermal state. Thus, real thermalization (if it occurs) should take a much longer time. This behavior has already been observed in other scenarios and is sometimes called ``prethermalization''. Finally, we compare our results to numerical simulations for finite lattices in one and two dimensions and find qualitative agreement.