Beats, broken-symmetry superfluid on a one dimensional anyon Hubbard model

Abstract

By using the density matrix renormalization group and mean field methods, the anyon Hubbard model is studied systematically on a one dimensional lattice. The model can be expressed as a Bose-Hubbard model with a density-dependent-phase term. When the phase angle is $\theta =0$ or $\theta =\pi$, the model will be equivalent to boson and pseudo fermion models, respectively. In the mean field frame, we find a broken-symmetry superfluid (BSF), in which the $b^{†}(b)$ operators on the nearest neighborhood sites have exactly opposite directions and behave like a directed oscillation pattern. By the density matrix reorganization group method, in the broken-symmetry superfluid, both the real and imaginary parts of the correlation $b_i^{†}{b}_{i+r}$ behave according to a {\it beat phenomenon} with $0<\theta <\pi$ in the form $C_0{e}^{ikr}(-1{)}^r$ or behave like waves with different wavelengths in the form $C_0{e}^{ikr}$. The distributions of the broken-symmetry superfluid phase and other phases are shown in the phase diagrams with different values of $\theta$ and the direct phase transition between the two types of superfluid is observed. The beats phenomenon is explained by double peaks of momentum distribution with two wave numbers $k_1$ and $k_2$ satisfying the condition $\frac{k_1-k_2}{k_1+k_2}<\frac{1}{3}$, which are expected to be observed in the optical experiments.

9 pages, 9 figures

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• The Anyon Hubbard Model in One-Dimensional Optical Lattices
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Cited by in corpus (1)

• Critical points of the anyon-Hubbard model