The large coordination number expansion of a lattice Bose gas at finite temperature

Abstract

The expansion of the partition function for large coordination number $Z$ is a long standing method and has formerly been used to describe the Ising model at finite temperatures. We extend this approach and study the interacting Bose gas at finite temperatures. An analytical expression for the free energy is derived which is valid for weakly interacting and strongly interacting bosons. The transition line which separates the superfluid phase from Mott insulating/normal gas phase is shown for fillings $⟨\hat{n}⟩=1$ and $⟨\hat{n}⟩=2$. For unit filling, our findings agree qualitatively with Quantum Monte-Carlo results. Contrary to the well-known mean-field result, the shift of the critical temperature in the weakly interacting regime is apparent.

6 pages, 5 figures (in press in Phys.Rev. A)

References in corpus (13)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Monte Carlo study of two-dimensional Bose-Hubbard model
• Formation of spatial shell structures in the superfluid to Mott insulator transition
• Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach
• Sweeping from the superfluid to Mott phase in the Bose-Hubbard model
• Boson Mott insulators at finite temperatures
• Ultracold bosons with short-range interaction in regular optical lattices
• Phase Diagram for Ultracold Bosons in Optical Lattices and Superlattices
• Bose-Hubbard phase diagram with arbitrary integer filling
• Mean-field phase diagram of disordered bosons in a lattice at non-zero temperature
• Bogoliubov theory of quantum correlations in the time-dependent Bose-Hubbard model
• The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study
• Finite-temperature effects on the superfluid Bose-Einstein condensation of confined ultracold atoms in three-dimensional optical lattices

Cited by in corpus (6)

• Doublon bottleneck in the ultrafast relaxation dynamics of hot electrons in 1T-TaS_2
• Boltzmann relaxation dynamics in the strongly interacting Fermi-Hubbard model
• Environment induced pre-thermalization in the Mott-Hubbard model
• Boltzmann relaxation dynamics of strongly interacting spinless fermions on a lattice
• Hierarchy of double-time correlations
• Attraction versus repulsion between doublons or holons in Mott-Hubbard systems