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arXiv:1207.2122 · Physical Review A

Tuning the Kosterlitz-Thouless transition to zero temperature in anisotropic boson systems

Jhih-Shih You, Hao Lee, Shiang Fang, Miguel A. Cazalilla, Daw-Wei Wang

Published Oct 10, 2012• 17 citations
arXivHTMLPDF

Abstract

We study the two-dimensional Bose-Hubbard model with anisotropic hopping. Focusing on the effects of anisotropy on superfluid properties such as 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., at a quantum critical point) and therefore quantum fluctuations play a dominant role, is particularly striking.

DOI
10.1103/physreva.86.043612

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Berezinskii--Kosterlitz--Thouless transition of the two-dimensional XYXYXY model on the honeycomb lattice
The Berezinskii--Kosterlitz--Thouless (BKT) transition of the two-dimensional XYXYXY model on the honeycomb lattice is investigated using both the techniques of Neural Network (NN) and Monte Carlo simulations. It is demonstrated in the literature that with certain plausible assumptions, the associated critical temperature TBKT,HT_{\text{BKT,H}}TBKT,H​ is found to be 12\frac{1}{\sqrt{2}}2​1​ exactly. Surprisingly, the value of TBKT,HT_{\text{BKT,H}}TBKT,H​ obtained from our NN calculations is 0.560(9) which deviates significantly from 12\frac{1}{\sqrt{2}}2​1​. In addition, based on the helicity modulus, the TBKT,HT_{\text{BKT,H}}TBKT,H​ determined is 0.571(8) agreeing well with that resulting from the NN estimation. The outcomes presented in this study indicate that a detailed analytic calculation is desirable to solve the found discrepancy.
Abstract The Berezinskii–Kosterlitz–Thouless (BKT) transition of the two-dimensional XYXYXY model on the honeycomb lattice is investigated using both the techniques of Neural network (NN) and Monte Carlo simulations. It is demonstrated in the literature that, with certain plausible assumptions, the associated critical temperature TBKT,HT_{\text{BKT,H}}TBKT,H​ is found to be 1/2{1}/{\sqrt{2}}1/2​ exactly. Surprisingly, the value of TBKT,HT_{\text{BKT,H}}TBKT,H​ obtained from our NN calculations is 0.572(3), which deviates significantly from 1/2{1}/{\sqrt{2}}1/2​. In addition, based on the helicity modulus, the TBKT,HT_{\text{BKT,H}}TBKT,H​ determined is 0.576(4), agreeing well with that resulting from the NN estimation. It will be interesting to carry out a more detailed analytic calculation to obtain a theoretical value consistent with the numerical result reached here.