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

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.

Title changed, new results added, references added

References in corpus (8)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Observation of Vortex Pinning in Bose-Einstein Condensates
• Degenerate Bose-Bose mixture in a three-dimensional optical lattice
• Quantum simulations of gauge theories with ultracold atoms: local gauge invariance from angular momentum conservation
• Detecting the Amplitude Mode of Strongly Interacting Lattice Bosons by Bragg Scattering
• Effective field theories for two-component repulsive bosons on lattice and their phase diagrams
• Bosonic t-J Model in a stacked triangular lattice and its phase diagram

Cited by in corpus (4)

• Phase diagrams of Bose-Hubbard model and Haldane-Bose-Hubbard model with complex hopping amplitudes
• Random-field-induced order in bosonic t-J model
• Superfluid, Supersolid and Checkerboard Solid in Two-Component Bosons in an Optical Lattice: Study by Means of Gross-Pitaevskii Theory and Monte-Carlo Simulations
• Ferromagnetic phase in the polarized two-species bosonic Hubbard Model