Bose-Einstein condensation and critical behavior of two-component bosonic gases

TL;DR

This paper investigates the critical behavior of two-component Bose-Einstein condensates in three dimensions, using field-theoretical RG methods, mean-field, and numerical simulations to identify universality classes and critical modes.

Contribution

It provides a comprehensive analysis of the universal critical behaviors and symmetry-breaking patterns in two-component bosonic gases at BEC transitions, supported by numerical simulations.

Findings

Critical behavior controlled by decoupled XY fixed point when both components condense

Different universality classes depending on symmetry breaking patterns

Slowly-decaying scaling corrections from inter-species interactions

Abstract

We study Bose-Einstein condensation (BEC) in three-dimensional two-component bosonic gases, characterizing the universal behaviors of the critical modes arising at the BEC transitions. For this purpose, we use field-theoretical (FT) renormalization-group (RG) methods and perform mean-field and numerical calculations. The FT RG analysis is based on the Landau-Ginzburg-Wilson Phi4 theory with two complex scalar fields which has the same symmetry as the bosonic system. In particular, for identical bosons with exchange Z_2,e symmetry, coupled by effective density-density interactions, the global symmetry is Z_2e X U(1) X U(1). At the BEC transition it may break into Z_2,e X Z_2 X Z_2 when both components condense simultaneously, or to U(1) X Z_2 when only one component condenses. This implies different universality classes for the corresponding critical behaviors. Numerical simulations of the two-component Bose-Hubbard model in the hard-core limit support the RG prediction: when both components condense simultaneously, the critical behavior is controlled by a decoupled XY fixed point, with unusual slowly-decaying scaling corrections arising from the on-site inter-species interaction.