Thermal Phase Transitions of Strongly Correlated Bosons with Spin-Orbit Coupling

Experiments on ultracold atomic gases have begun to explore lattice effects and thermal fluctuations for two-component bosons with spin-orbit coupling (SOC). Motivated by this, we study a $tJ$ model of strongly correlated lattice bosons, with equal Rashba-Dresselhaus SOC and a uniform magnetic field. At zero temperature, a Gutzwiller ansatz is shown to capture lattice variants of stripe superfluid (SF) ground states. We formulate a finite temperature generalization of the Gutzwiller approach and show that thermal fluctuations in the doped Mott insulator drive a two-step melting of the stripe SF, revealing a wide intermediate regime of a normal fluid with stripe order.