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arXiv:2204.07739 · Physical review. B./Physical review. B

Quantum phase diagram for two-species hardcore bosons in one-dimensional optical lattices with resonantly driven Rabi frequency

Peigeng Zhong, Tao Wang, Shijie Hu, Hai‐Qing Lin

Published Jul 21, 2022• 2 citations
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Abstract

Following a proposed scheme for realizing the time-periodically modulated Rabi frequency in experiments, we suggest density-dependent hoppings of two-species hardcore bosons in a one-dimensional optical lattice. Distinct from the previous work [Phys. Rev. Res. 2, 013275 (2020)], we study effects in the first resonance region. In the effective Hamiltonian, the intraspecies hopping occurs only if the density discrepancy of the other species on these sites is zero, while the interspecies one is allowed once the relevant density discrepancy becomes nonzero. At integer-1 filling, the quantum phase diagram of the effective Hamiltonian is determined by the perturbation analysis together with numerical calculations. We find that in the limit of dominant ${J}_{1}$, the system becomes a double-degenerate dimerized state spontaneously breaking the translation symmetry. The interplay of ${J}_{0}, {J}_{1}$, and the fixed $\overline{U}=1$ leads to three BKT transition lines and a tricritical BKT point. Exact transition lines are obtained by the level spectroscopic technique. Besides, general physical properties, including the charge gap, neutral gap, superfluid density, and dimerization strength, are investigated as well.

DOI
10.1103/physrevb.106.045130

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Following a proposed scheme for realizing the time-periodically modulated Rabi frequency in experiments, we suggest density-dependent hoppings of two-species hardcore bosons in a one-dimensional optical lattice. Distinct from the previous work [Phys. Rev. Res. 2, 013275 (2020)], we study effects in the first resonance region. In the effective Hamiltonian, the intraspecies hopping occurs only if the density discrepancy of the other species on these sites is zero, while the interspecies one is allowed once the relevant density discrepancy becomes nonzero. At integer-1 filling, the quantum phase diagram of the effective Hamiltonian is determined by the perturbation analysis together with numerical calculations. We find that in the limit of dominant J1{J}_{1}J1​, the system becomes a double-degenerate dimerized state spontaneously breaking the translation symmetry. The interplay of J0,J1{J}_{0}, {J}_{1}J0​,J1​, and the fixed U‾=1\overline{U}=1U=1 leads to three BKT transition lines and a tricritical BKT point. Exact transition lines are obtained by the level spectroscopic technique. Besides, general physical properties, including the charge gap, neutral gap, superfluid density, and dimerization strength, are investigated as well.
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Using worm-type quantum Monte Carlo simulations, we investigate bosonic mixtures on a triangular lattice of two species of bosons, which interact via nearest-neighbor intraspecies (VVV) and on-site interspecies (UUU) repulsions. For the case of symmetric hopping amplitude (tA/V=tB/V{t}_{A}/V={t}_{B}/VtA​/V=tB​/V) and U/V=1U/V=1U/V=1, we determine a rich ground-state phase diagram that contains double-solid, double-superfluid, supersolid (SS), solid-superfluid (solid-SF), and counterflow supersolid (CSS) states. The SS, solid-SF, and CSS states exhibit spontaneous symmetry breaking among the three sublattices of the triangular lattice and between the two species, which leads to a nonzero crystalline density wave order in each species. We, furthermore, show that the CSS and the SS states are present for ${t}_{A}/V\ensuremath{\ne}{t}_{B}/V$, and the latter even survives up to the ${t}_{A}/V\ensuremath{\rightarrow}\ensuremath{\infty}$ or ${t}_{B}/V\ensuremath{\rightarrow}\ensuremath{\infty}$ limit. The effects induced by the variation of U/VU/VU/V and by the imbalance of particle numbers of the two species are also explored.
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.
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