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arXiv:1802.08104 · Physical review. B./Physical review. B

Extended Bose-Hubbard model with dipolar and contact interactions

Krzysztof Biedroń, Mateusz Łącki, Jakub Zakrzewski

Published Jun 5, 2018• 36 citations
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Abstract

We study the phase diagram of the one-dimensional boson gas trapped inside an optical lattice with contact and dipolar interaction, taking into account next-nearest terms for both tunneling and interaction. Using the density-matrix renormalization group, we calculate how the locations of phase transitions change with increasing dipolar interaction strength for average density $\ensuremath{\rho}=1$. Furthermore, we show the emergence of pair-correlated phases for a large dipolar interaction strength and $\ensuremath{\rho}\ensuremath{\ge}2$, including a supersolid phase with an incommensurate density wave ordering manifesting the corresponding spontaneous breaking of the translational symmetry.

DOI
10.1103/physrevb.97.245102

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We study the phase diagram of the one-dimensional boson gas trapped inside an optical lattice with contact and dipolar interaction, taking into account next-nearest terms for both tunneling and interaction. Using the density-matrix renormalization group, we calculate how the locations of phase transitions change with increasing dipolar interaction strength for average density \ensuremathρ=1\ensuremath{\rho}=1\ensuremathρ=1. Furthermore, we show the emergence of pair-correlated phases for a large dipolar interaction strength and \ensuremathρ\ensuremath≥2\ensuremath{\rho}\ensuremath{\ge}2\ensuremathρ\ensuremath≥2, including a supersolid phase with an incommensurate density wave ordering manifesting the corresponding spontaneous breaking of the translational symmetry.
We theoretically analyze the phase diagram of a quantum gas of bosons that interact via repulsive dipolar interactions. The bosons are tightly confined by an optical lattice in a quasi-one-dimensional geometry. In the single-band approximation, their dynamics is described by an extended Bose-Hubbard model where the relevant contributions of the dipolar interactions consist of density-density repulsion and correlated tunneling terms. We evaluate the phase diagram for unit density using numerical techniques based on the density-matrix renormalization group algorithm. Our results predict that correlated tunneling can significantly modify the parameter range of the topological insulator phase. At vanishing values of the onsite interactions, moreover, correlated tunneling promotes the onset of a phase with a large number of low-energy metastable configurations.
We study the extended Bose-Hubbard model describing an ultracold gas of dipolar molecules in an optical lattice, taking into account all on-site and nearest-neighbor interactions, including occupation-dependent tunneling and pair tunneling terms. Using exact diagonalization and the multiscale entanglement renormalization ansatz, we show that these terms can destroy insulating phases and lead to novel quantum phases. These considerable changes of the phase diagram have to be taken into account in upcoming experiments with dipolar molecules.
We determine the quantum ground state of dipolar bosons in a quasi-one-dimensional optical lattice and interacting via sss-wave scattering. The Hamiltonian is an extended Bose-Hubbard model which includes hopping terms due to the interactions. We identify the parameter regime for which the coefficients of the interaction-induced hopping terms become negative. For these parameters we numerically determine the phase diagram for a canonical ensemble and by means of density matrix renormalization group. We show that at sufficiently large values of the dipolar strength there is a quantum interference between the tunneling due to single-particle effects and the one due to the interactions. Because of this phenomenon, incompressible phases appear at relatively large values of the single-particle tunneling rates. This quantum interference cuts the phase diagram into two different, disconnected superfluid phases. In particular, at vanishing kinetic energy, the phase is always superfluid with a staggered superfluid order parameter. These dynamics emerge from quantum interference phenomena between quantum fluctuations and interactions and shed light into their role in determining the thermodynamic properties of quantum matter.
Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin et al., Nature (London) 609, 485 (2022)], we study a one-dimensional version of the two-component extended Bose-Hubbard model via the density-matrix renormalization group method. By using the nearest-neighbor and on-site interaction parameters from the experiment, we start by mapping the quantum phase diagram in the hopping parameter ${t}_{A}\text{\ensuremath{-}}{t}_{B}$ plane with boson densities ${\ensuremath{\rho}}_{A}={\ensuremath{\rho}}_{B}=1/2$. In addition to the density-wave phase reported in the experiment, we find several regimes of superfluidity when one or both hopping parameters are large enough, and interestingly there is a supercounterfluid phase at moderate and comparable hopping parameters. The universality classes of these phase transitions are analyzed from the correlation functions, excitation gaps, and entanglement entropy. In particular, a Berezinskii-Kosterlitz-Thouless type is recognized for several gapped-to-gapless transitions. In addition, we also study the quantum phase transitions by varying ${\ensuremath{\rho}}_{B}$ from 0 to 1 while keeping ${\ensuremath{\rho}}_{A}=1/2$. We identify a supersolid phase in a wide range of $1/2<{\ensuremath{\rho}}_{B}<1$. Our work paves the way for realizing exotic many-body phases in cold-atom experiments upon proper tuning of experimental parameters.
We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil’s staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square and triangular lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.
We study the one-dimensional extended Bose-Hubbard model in incommensurate densities using the density matrix renormalization group with the mean-filed (CMFT+DMRG)and density matrix renormalization group (DMRG) methods. We focus on the region of the phase diagram where onsite interaction (U) is smaller than the nearest-neighbor interaction (V). We determine the superfluid and the density wave order parameters to identify superfluid, phase-separated, supersolid, density wave phases, and obtain the phase diagram in the density-onsite interaction(ρ, U) plane for fixed nearest-neighbor interaction. The supersolid and phase-separation phases exist for a wide range of densities. The density ranges for which the phase-separation is seen shrinking with theincrease in the onsite interaction.