Capturing the re-entrant behaviour of one-dimensional Bose-Hubbard model

TL;DR

This paper investigates the re-entrant phase transition behavior in the one-dimensional Bose-Hubbard model, demonstrating that real-space renormalization group methods uniquely capture this phenomenon among common approximations.

Contribution

It shows for the first time that the real-space RG approach can accurately reproduce the re-entrant phase transition in the 1D Bose-Hubbard model, unlike mean-field and cluster methods.

Findings

Mean-field calculations do not reproduce re-entrance.

Finite-sized clusters show a precursor to re-entrance.

Real-space RG captures the re-entrant behavior successfully.

Abstract

The Bose Hubbard model (BHM) is an archetypal quantum lattice system exhibiting a quantum phase transition between its superfluid (SF) and Mott-insulator (MI) phase. Unlike in higher dimensions the phase diagram of the BHM in one dimension possesses regions in which increasing the hopping amplitude can result in a transition from MI to SF and then back to a MI. This type of re-entrance is well known in classical systems like liquid crystals yet its origin in quantum systems is still not well understood. Moreover, this unusual re-entrant character of the BHM is not easily captured in approximate analytical or numerical calculations. Here we study in detail the predictions of three different and widely used approximations; a multi-site mean-field decoupling, a finite-sized cluster calculation, and a real-space renormalization group (RG) approach. It is found that mean-field calculations do not reproduce re-entrance while finite-sized clusters display a precursor to re-entrance. Here we show for the first time that RG does capture the re-entrant feature and constitutes one of the simplest approximation able to do so. The differing abilities of these approaches reveals the importance of describing short-ranged correlations relevant to the kinetic energy of a MI in a particle-number symmetric way.