Quantum criticality of a Bose gas in an optical lattice near the Mott transition

TL;DR

This paper investigates the quantum critical behavior of a Bose gas in an optical lattice near the Mott transition, deriving an equation of state and calculating effective parameters using a nonperturbative renormalization-group approach.

Contribution

It introduces a method to compute the renormalized mass and scattering length near the Mott transition within the Bose-Hubbard model using nonperturbative techniques.

Findings

Derived the equation of state near the Mott transition.

Calculated the effective mass and scattering length at the quantum critical point.

Showed the similarity to a dilute Bose gas with renormalized parameters.

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 P({\mu},T) versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass m^* and scattering length a^*. m^* 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 a^* 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 t/U between hopping amplitude and on-site repulsion.