Abstract
We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass and scattering length . Here is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott-insulating phase, while is related to their effective interaction at low energy. We use a nonperturbative renormalization-group approach to compute these parameters as a function of the ratio between hopping amplitude and on-site repulsion.
- Received 8 July 2011
DOI:https://doi.org/10.1103/PhysRevA.85.011602
©2012 American Physical Society