Non-perturbative renormalization-group approach to the Bose-Hubbard model

TL;DR

This paper introduces a non-perturbative renormalization-group method for the Bose-Hubbard model, accurately capturing phase transitions and critical behavior by incorporating local and long-range fluctuations.

Contribution

It develops a novel RG approach starting from decoupled sites, effectively describing both local and long-distance fluctuations in the Bose-Hubbard model.

Findings

Accurately reproduces the phase diagram in agreement with quantum Monte Carlo results.

Captures the two universality classes of the superfluid--Mott-insulator transition.

Identifies the Ginzburg length as a key crossover scale.

Abstract

We present a non-perturbative renormalization-group approach to the Bose-Hubbard model. By taking as initial condition of the RG flow the (local) limit of decoupled sites, we take into account both local and long-distance fluctuations in a nontrivial way. This approach yields a phase diagram in very good quantitative agreement with the quantum Monte Carlo results and reproduces the two universality classes of the superfluid--Mott-insulator transition with a good estimate of the critical exponents. Furthermore, it reveals the crucial role of the "Ginzburg length" as a crossover length between a weakly- and a strongly-correlated superfluid phase.