Finite-temperature degenerate perturbation theory for bosons in optical lattices
Abstract
Bosonic atoms confined in optical lattices can exist in two different phases, Mott-insulator and superfluid, depending on the strength of the system parameters, such as the on-site interaction between particles and the hopping parameter. This work is motivated by the fact that non-degenerate perturbation theory applied to the mean-field approximation of the Bose-Hubbard Hamiltonian at zero and finite temperature fails to give consistent results in the vicinity of the Mott-insulator-superfluid phase transition, e.g., the order parameter calculated via non-degenerate perturbation theory reveals an unphysical behavior between neighboring Mott lobes, which is an explicit consequence of degeneracy problems that artificially arise from such a treatment. Therefore, in order to fix this problem, we propose a finite-temperature degenerate perturbation theory approach based on a projection operator formalism which ends up solving such degeneracy problems in order to obtain physically consistent results for the order parameter near the phase transition.
Keywords
Cite
@article{arxiv.1906.09661,
title = {Finite-temperature degenerate perturbation theory for bosons in optical lattices},
author = {Felipe Taha Sant'Ana and Axel Pelster and Francisco Ednilson Alves dos Santos},
journal= {arXiv preprint arXiv:1906.09661},
year = {2019}
}