2013/11/30 by F. Queisser, K. V. Krutitsky, P. Navez +1
Physics and Astronomy · #quant-ph #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.89.033616
published as Phys.Rev.A 89, 033616 (2014) · arXiv admin note: substantial text overlap with arXiv:1203.2164
arxiv created 2014/03/22 · arxiv updated 2014/03/25
We study the Bose and Fermi Hubbard model in the (formal) limit of large coordination numbers Z≫1. Via an expansion into powers of 1/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 J 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 cannot be described by a thermal state. Thus, real thermalization (if it occurs) should take much longer time. This behavior has already been observed in other scenarios and is sometimes called ``pre-thermalization.'' Finally, we compare our results to numerical simulations for finite lattices in one and two dimensions and find qualitative agreement.