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.
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 two-dimensional square lattice hard-core boson Hubbard model with near-neighbor interactions has a ``checkerboard'' charge density wave insulating phase at half filling and sufficiently large intersite repulsion. When doped, rather than forming a supersolid phase in which long-range charge density wave correlations coexist with a condensation of superfluid defects, the system instead phase separates. However, it is known that there are other lattice geometries and interaction patterns for which such coexistence takes place. In this paper we explore the possibility that anisotropic hopping or anisotropic near-neighbor repulsion might similarly stabilize the square lattice supersolid. By considering the charge density wave structure factor and superfluid density for different ratios of interaction strength and hybridization in the $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{y}$ directions, we conclude that phase separation still occurs.
By using an unbiased quantum Monte Carlo method, we investigate the hard-core Bose-Hubbard model on a square lattice with the anisotropic dipole-dipole interaction. To study the effect of the anisotropy, dipole moments are assumed to be polarized in the y direction on the two-dimensional xy plane. To perform efficient simulations of long-range interacting systems, we use the worm algorithm with an O(N) Monte Carlo method. We obtain the ground-state phase diagram that includes a superfluid phase and a striped solid phase at half-filling as two main phases. In addition to these two main phases, we find a small region where there are multiple plateaus in the particle density for small hopping amplitudes. In this region, the number of plateaus increases as the system size increases. This indicates the appearance of numerous competing ground states due to frustrated interactions. In our simulations, we find no evidence of a supersolid phase.
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.
The cold atom on a two-dimensional square optical lattice is studied within the hard-core boson Hubbard model with an alternating potential. In terms of the quantum Monte Carlo method, it is shown explicitly that a supersolid phase emerges due to the presence of the alternating potential. For the weak alternating potential, the supersolid state appears for the whole range of hard-core boson densities except the half-filling case, where the system is a Mott insulator. However, for the strong alternating potential, besides the supersolid and Mott insulating states, a charge-density wave phase appears.
We study the phase diagram of a system of soft-core dipolar bosons confined to a two-dimensional optical lattice layer. We assume that dipoles are aligned perpendicular to the layer such that the dipolar interactions are purely repulsive and isotropic. We consider the full dipolar interaction and perform Path Integral Quantum Monte Carlo simulations using the Worm Algorithm. Besides a superfluid phase, we find various solid and supersolid phases. We show that, unlike what was found previously for the case of nearest-neighboring interaction, supersolid phases are stabilized not only by doping the solids with particles but with holes as well. We further study the stability of these quantum phases against thermal fluctuations. Finally, we discuss pair formation and the stability of the pair checkerboard phase formed in a bilayer geometry, and suggest experimental conditions under which the pair checkerboard phase can be observed.
In this paper, we study an extended bosonic t-J model in an optical lattice, which describes two-component hard-core bosons with nearest-neighbor pseudospin interactions and, also, inter- and intraspecies dipole-dipole interactions. In particular, we focus on the case in which two-component hard-core bosons have antiparallel polarized dipoles with each other. The global phase diagram is studied by means of the Gutzwiller variational method and also quantum Monte Carlo (QMC) simulations. Both calculations show that a striped solid order, besides a checkerboard one, appears as a result of the dipole-dipole interactions. By QMC, we find that two kinds of supersolids (SSs) form, i.e., checkerboard SS and striped SS, and we also verify the existence of an exotic phase between the striped solid and the checkerboard SS. Finally, by QMC, we study the t-J-like model, which was recently realized experimentally by A. de Paz et al. [Phys. Rev. Lett. 111, 185305 (2013)].