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arXiv:2604.25694

Magnetic quantum phases of spin-orbit-coupled anisotropic dipolar bosons in square lattices

Nitin Kaloya, Kuldeep Suthar

Published Apr 28, 2026• 0 citations
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Abstract

We examine the two-dimensional spin-orbit-coupled bosons in the presence of an anisotropic dipolar interaction in square lattices. The spin-orbit coupling leads to finite-momentum superfluid and supersolid states, while the nearest-neighbour interaction induces crystalline characteristics in the quantum phases of soft-core bosons. We employ site-decoupled Gutzwiller ansatz and mean-field decoupling theory to obtain the phase diagrams and investigate the effects of the tilt of magnetic dipoles with respect to the polarization axis. Our study reveals the intriguing quantum phase transition of checkerboard finite-momentum phase-twisted and phase-stripe states into their stripe counterparts at a magic tilt angle, at which the off-site interaction along one of the directions becomes zero. At smaller tilt angles, the checkerboard charge-density-wave phase intervened by two compressible finite-momentum phases, and at strong spin-orbit coupling strengths, the phase-twisted supersolid and superfluid phases emerge. At larger tilt angles, a transition between the striped order of phase-twisted states and phase-stripe states occurs. The inclusion of off-site inter-component correlation leads to density-correlated phases, lattice-induced supersolid, and ferromagnetic quantum phases. Our study highlights novel finite-momentum crystal phases of spin-orbit-coupled dipolar bosons and provides a parameter space to observe them in quantum gas experiments.

DOI
10.48550/arxiv.2604.25694

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We examine the two-dimensional spin-orbit-coupled bosons in the presence of an anisotropic dipolar interaction in square lattices. The spin-orbit coupling leads to finite-momentum superfluid and supersolid states, while the nearest-neighbour interaction induces crystalline characteristics in the quantum phases of soft-core bosons. We employ site-decoupled Gutzwiller ansatz and mean-field decoupling theory to obtain the phase diagrams and investigate the effects of the tilt of magnetic dipoles with respect to the polarization axis. Our study reveals the intriguing quantum phase transition of checkerboard finite-momentum phase-twisted and phase-stripe states into their stripe counterparts at a magic tilt angle, at which the off-site interaction along one of the directions becomes zero. At smaller tilt angles, the checkerboard charge-density-wave phase intervened by two compressible finite-momentum phases, and at strong spin-orbit coupling strengths, the phase-twisted supersolid and superfluid phases emerge. At larger tilt angles, a transition between the striped order of phase-twisted states and phase-stripe states occurs. The inclusion of off-site inter-component correlation leads to density-correlated phases, lattice-induced supersolid, and ferromagnetic quantum phases. Our study highlights novel finite-momentum crystal phases of spin-orbit-coupled dipolar bosons and provides a parameter space to observe them in quantum gas experiments.
Abstract We investigate the quantum phases and phase transitions for spin–orbit coupled two-species bosons with nearest-neighbor (NN) interaction in a two-dimensional square lattice using inhomogeneous dynamical Guztwiller mean-field method. Under the effect of spin–orbit coupling and NN interaction, we uncover a rich variety of different magnetic supersolid (SS) phases. In the presence of intraspecies NN interaction, the phase diagram exhibits the phase-twisted double-checkerboard SS (PT-DCSS) and phase-striped double-checkerboard SS (PS-DCSS) phases. For both intra- and interspecies NN interactions, apart from the phase-twisted lattice SS (PT-LSS) and phase-striped lattice SS (PS-LSS) phases, some nontrivial SS phases with interesting properties occur. More importantly, we find that the emergences of these nontrivial SS phases are dependent of the interspecies on-site interaction. To further characterize the SS phases, we also discuss the spin-dependent momentum distributions and magnetic textures. The magnetic textures, such as antiferromagnetic, spiral and stripe orders are shown. Finally, we give the fully analytical insights into the numerical results.
We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle $\ensuremath{\theta}$ of the dipolar bosons. At low tilt angles, ${0}^{\ensuremath{\circ}}\ensuremath{\leqslant}\ensuremath{\theta}\ensuremath{\lesssim}{25}^{\ensuremath{\circ}}$, the ground states of the system are phases with checkerboard order, which can be either checkerboard supersolids or checkerboard density waves. For high tilt angles, ${35}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{55}^{\ensuremath{\circ}}$, phases with striped order of the supersolid or density wave are preferred. In the intermediate domain, ${25}^{\ensuremath{\circ}}\ensuremath{\lesssim}\ensuremath{\theta}\ensuremath{\lesssim}{35}^{\ensuremath{\circ}}$, an emulsion or superfluid phase intervenes the transition between the checkerboard and the striped phases. The attractive interaction dominates at $\ensuremath{\theta}\ensuremath{\gtrsim}{55}^{\ensuremath{\circ}}$, which renders the system unstable, and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second-order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results. In our study, the incompressible phases have an average occupancy per site $\ensuremath{\rho}\ensuremath{\le}1$, but the compressible phases can have $\ensuremath{\rho}>1$.
Motivated by recent experiments with ultracold magnetic atoms trapped in optical lattices where the orientation of atomic dipoles can be fully controlled by external fields, we study the ground state properties of dipolar bosons trapped in a two-dimensional lattice with density-induced hopping and where the dipoles are tilted along the xzxzxz plane. We present ground state phase diagrams of the above system at different tilt angles. We find that, as the dipolar interaction increases, the superfluid phase at half filling factor is destroyed in favor of either a checkerboard or stripe solid phase for tilt angle θ≲35.3∘\theta \lesssim 35.3^{\circ}θ≲35.3∘ or θ≳35.3∘\theta \gtrsim 35.3^{\circ}θ≳35.3∘ respectively. More interesting physics happens at tilt angles θ≳58∘\theta \gtrsim 58^{\circ}θ≳58∘ where we find that, as the dipolar interaction strength increases, solid phases first appear at filling factor lower than 0.50.50.5. Moreover, unlike what observed at lower tilt angles at half filling, we find that the superfluid gives way to a stripe solid through a stripe supersolid phase.
Motivated by recent experiments with ultracold magnetic atoms trapped in optical lattices where the orientation of atomic dipoles can be fully controlled by external fields, we study, by means of quantum Monte Carlo, the ground-state properties of dipolar bosons trapped in a two-dimensional lattice with density-induced hopping and where the dipoles are tilted along the xzxzxz plane. We present ground-state phase diagrams of the above system at different tilt angles. We find that as the dipolar interaction increases, the superfluid phase at half-filling factor is destroyed in favor of either a checkerboard or stripe solid phase for tilt angle $\ensuremath{\theta}\ensuremath{\lesssim}{30}^{\ensuremath{\circ}}$ or $\ensuremath{\theta}\ensuremath{\gtrsim}{30}^{\ensuremath{\circ}}$, respectively. More interesting physics happens at tilt angles $\ensuremath{\theta}\ensuremath{\gtrsim}{58}^{\ensuremath{\circ}}$, where we find that as the dipolar interaction strength increases, solid phases first appear at filling factor lower than 0.5. Moreover, unlike what is observed at lower tilt angles, we find that at half filling, a stripe supersolid intervenes between the superfluid and stripe solid phase.
We show anisotropy of the dipole interaction between magnetic atoms or polar molecules can stabilize new quantum phases in an optical lattice. Using a well-controlled numerical method based on the tensor network algorithm, we calculate the phase diagram of the resultant effective Hamiltonian in a two-dimensional square lattice---an anisotropic Hubbard model of hard-core bosons with attractive interaction in one direction and repulsive interaction in the other direction. Besides the conventional superfluid and the Mott insulator states, we find the striped and the checkerboard charge-density-wave states and the supersolid phase that interconnect the superfluid and the striped solid states. The transition to the supersolid phase has a mechanism different from the case of the soft-core Bose-Hubbard model.
The recent advances in creating nearly degenerate quantum dipolar gases in optical lattices are opening the doors for the exploration of equilibrium physics of quantum systems with anisotropic and long-range dipolar interactions. In this paper we study the zero- and finite-temperature phase diagrams of a system of hard-core dipolar bosons at half-filling, trapped in a two-dimensional square optical lattice. The dipoles are aligned parallel to one another and tilted out of the optical lattice plane by means of an external electric field. At zero-temperature, the system is a superfluid (SF) at all tilt angles θ provided that the strength of dipolar interaction is below a critical value . Upon increasing the interaction strength while keeping θ fixed, the SF phase is destabilized in favor of a checkerboard or a stripe solid (SS) depending on the tilt angle. We explore the nature of the phase transition between the two solid phases, identifying a region of metastable emulsion states intervening between the two solid lobes. Additionally, we study the stability of these quantum phases against thermal fluctuations and find that the SS is the most robust, making it the best candidate for experimental observation.