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arXiv:1312.6737 · Physical Review B

Dynamics of the Bose-Hubbard chain for weak interactions

Martin L. R. Fürst, Christian B. Mendl, Herbert E. Spohn

Published Apr 30, 2014• 1 citation
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Abstract

We study the Boltzmann transport equation for the Bose-Hubbard chain in the kinetic regime. The time-dependent Wigner function is matrix-valued with odd dimension due to integer spin. For nearest neighbor hopping only, there are infinitely many additional conservation laws and nonthermal stationary states. Adding longer-range hopping amplitudes entails exclusively thermal equilibrium states. Especially for small next-nearest neighbor hopping amplitudes, we observe prethermalization with two time scales, which can be related to the relative strength of the nearest and next-nearest hopping. We provide a derivation of the Boltzmann equation based on the Hubbard Hamiltonian, including general interactions beyond on-site, and illustrate the results by numerical simulations.

DOI
10.1103/physrevb.89.134311

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We consider a fermionic Hubbard chain with an additional next-to-nearest neighbor hopping term. We study the thermalization rates of the quasimomentum distribution function within a quantum Boltzmann equation approach. We find that the thermalization rates are proportional to the square of the next-to-nearest neighbor hopping: Even weak next-to-nearest neighbor hopping in addition to nearest neighbor hopping leads to thermalization in a two-particle scattering quantum Boltzmann equation in one dimension. We also investigate the temperature dependence of the thermalization rates, which away from half filling become exponentially small for small temperature of the final thermalized distribution.
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