Effective field theory for two-species bosons in an optical lattice: Multiple order, the Nambu-Goldstone bosons, the Higgs mode and vortex lattice

TL;DR

This paper develops an effective field theory for a two-species bosonic system in an optical lattice, analyzing phase diagrams, low-energy excitations, and vortex lattice formations, with implications for cold atom experiments.

Contribution

It derives a comprehensive effective field theory for the two-species bosonic XY model, including multiple order parameters, Nambu-Goldstone bosons, the Higgs mode, and vortex lattice phenomena.

Findings

Identification of multiple order phases including Bose-Einstein condensates

Derivation of the effective field theory describing low-energy excitations

Observation of vortex lattice formation under effective magnetic fields

Abstract

In the previous papers, we studied the bosonic t-J mode and derived an effective field theory, which is a kind of quantum XY model. The bosonic t-J model is expected to be realized by experiments of two-component cold atoms in an optical lattice. In this paper, we consider a similar XY model that describes phase diagram of the t-J model with a mass difference. Phase diagram and critical behavior of the quantum XY model are clarified by means of the Monte-Carlo simulations. Effective field theory that describes the phase structure and low-energy excitations of the quantum XY model is derived. Nambu-Goldstone bosons and the Higgs mode are studied by using the effective field theory and interesting findings are obtained for the system with multiple order, i.e., Bose-Einstein condensations and pseudo-spin symmetry. We also investigate physical properties of the quantum XY model in an effective magnetic field that is realized by rotating the optical lattice, etc. We show that low-energy states of the system strongly depend on the strength of the "magnetic field". For some specific strength of the magnetic field, vortex lattice forms and the correlation function of the bosons exhibits solid like behavior, which is a kind of Bose-Einstein condensation.