Density matrix renormalization group study of the Anyon-Hubbard model

3rd International Meeting for Researchers in Materials and Plasma Technology; 1st Symposium on Nanoscience and Nanotechnology

物理学;材料科学

Arcila-Forero, J.^1 ; Franco, R.^1 ; Silva-Valencia, J.^1

Universidad Nacional de Colombia, Bogotá, Colombia^1

关键词: Bose Hubbard model;    Computational physics;    Density matrix renormalization group;    Density matrix renormalization group methods;    Many-body problems;    Particle exchange;    Two-body interactions;    Universality class;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/687/1/012064/pdf
DOI  :  10.1088/1742-6596/687/1/012064

学科分类：材料科学（综合）

来源: IOP

【 摘 要 】

Recently optical lattices allow us to observe phase transition without the uncertainty posed by complex materials, and the simulations of these systems are an excellent bridge between materials-based condensed matter physics and cold atoms. In this way, the computational physics related to many-body problems have increased in importance. Using the density matrix renormalization group method, we studied a Hubbard model for anyons, which is an equivalent to a variant of the Bose-Hubbard model in which the bosonic hopping depends on the local density. This is an exact mapping between anyons and bosons in one dimension. The anyons interlope between bosons and fermions. For two anyons under particle exchange, the wave function acquires a fractional phase eiθ. We conclude that this system exhibits two phases: Mott-insulator and superfluid. We present the phase diagram for some angles. The Mott lobe increases with an increase of the statistical. We observed a reentrance phase transition for all lobes. We showed that the model studied is in the same universality class as the Bose-Hubbard model with two-body interactions.