Tuning the Kosterlitz-Thouless transition to zero temperature in Anisotropic Boson Systems

TL;DR

This paper investigates how anisotropy affects the superfluid transition in a 2D Bose-Hubbard model, demonstrating that the self-consistent harmonic approximation accurately captures the transition, especially near the quantum critical point where the transition temperature approaches zero.

Contribution

It compares Quantum Monte Carlo simulations with the self-consistent harmonic approximation to analyze anisotropic effects on superfluid properties and the BKT transition in the 2D Bose-Hubbard model.

Findings

SCHA provides a good description of superfluid properties with proper formulation.

The accuracy of SCHA is high in the extremely anisotropic limit.

The BKT transition temperature can be tuned to zero, indicating a quantum critical point.

Abstract

We study the two-dimensional Bose-Hubbard model with anisotropic hopping. Focusing on the effects of anisotropy on the superfluid properties such like the helicity modulus and the normal-to-superfluid (Berezinskii-Kosterlitz-Thouless, BKT) transition temperature, two different approaches are compared: Large-scale Quantum Monte Carlo simulations and the self-consistent harmonic approximation (SCHA). For the latter, two different formulations are considered, one applying near the isotropic limit and the other applying in the extremely anisotropic limit. Thus we find that the SCHA provides a reasonable description of superfluid properties of this system provided the appropriate type of formulation is employed. The accuracy of the SCHA in the extremely anisotropic limit, where the BKT transition temperature is tuned to zero (i.e. into a Quantum critical point) and therefore quantum fluctuations play a dominant role, is particularly striking.