Magnetic order, Bose-Einstein condensation, and superfluidity in a bosonic t-J model of CP^1 spinons and doped Higgs holons

TL;DR

This paper explores the phase diagram of a 3D bosonic t-J model with CP^1 spinons and Higgs holons, revealing coexistence of antiferromagnetic order and Bose-Einstein condensation through Monte Carlo simulations.

Contribution

It introduces a lattice gauge theory model combining AF order and holon BEC, analyzing their interplay via Monte Carlo methods in both 2D and 3D settings.

Findings

AF order and BEC coexist at low temperatures and certain hole densities in 3D.

Phase diagram in 2D shows similar coexistence and transitions.

Implications for cold atom systems and strongly correlated electron models.

Abstract

We study the three-dimensional U(1) lattice gauge theory of a CP$^1$ spinon (Schwinger boson) field and a Higgs field. It is a bosonic $t$-$J$ model in slave-particle representation, describing the antiferromagnetic (AF) Heisenberg spin model with doped bosonic holes expressed by the Higgs field. The spinon coupling term of the action favors AF long-range order, whereas the holon hopping term in the ferromagnetic channel favors Bose-Einstein condensation (BEC) of holons. We investigate the phase structure by means of Monte-Carlo simulations and study an interplay of AF order and BEC of holes. We consider the two variations of the model; (i) the three-dimensional model at finite temperatures, and (ii) the two-dimensional model at vanishing temperature. In the model (i) we find that the AF order and BEC coexist at low temperatures and certain hole concentrations. In the model (ii), by varying the hole concentration and the stiffness of AF spin coupling, we find a phase diagram similar to the model (i). Implications of the results to systems of cold atoms and the fermionic $t$-$J$ model of strongly-correlated electrons are discussed.