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Fortschritte der Physik

Engineering Quantum Phases of Ultracold Bosons on Lieb Lattice

Yang Lin

Published Dec 21, 2024• 0 citations
Publisher

Abstract

Abstract The quantum phase transition of the hardcore boson model on a Lieb lattice by quantum Monte Carlo simulations is studied. Considering nearest‐neighbor interchain hopping, the phase diagram of the Bose‐Hubbard model on the Lieb lattice contains solid phases with average density = 2/3, and superfluid phases between solid phases.Two ways of controlling quantum states are discussed: to add an alternating on‐site potential, and to add an alternating hopping amplitude in the X‐ and Y‐directions. For the above cases, there exists a new filling state, = 1/3. Adding an alternating on‐site potential to the Hamiltonian, the phase transition from to is sharp and discontinuous, featuring the nature of a first order. Considering a dimerization term, for large V, it is expected that there is a direct transition from the valence‐bond insulator to the CDW as the interaction is strengthened. For the three cases, upper boundary for and lower boundary for are calculated.

DOI
10.1002/prop.202300235

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Abstract The quantum phase transition of the hardcore boson model on a Lieb lattice by quantum Monte Carlo simulations is studied. Considering nearest‐neighbor interchain hopping, the phase diagram of the Bose‐Hubbard model on the Lieb lattice contains solid phases with average density = 2/3, and superfluid phases between solid phases.Two ways of controlling quantum states are discussed: to add an alternating on‐site potential, and to add an alternating hopping amplitude in the X‐ and Y‐directions. For the above cases, there exists a new filling state, = 1/3. Adding an alternating on‐site potential to the Hamiltonian, the phase transition from to is sharp and discontinuous, featuring the nature of a first order. Considering a dimerization term, for large V, it is expected that there is a direct transition from the valence‐bond insulator to the CDW as the interaction is strengthened. For the three cases, upper boundary for and lower boundary for are calculated.
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 investigate interacting bosons on a two-dimensional Lieb lattice, taking into account kinetic tunneling terms between the nearest-neighboring and next-nearest-neighboring sites. In the frame of a time-dependent variational Gutzwiller method, ground states of the Bose–Hubbard model are accessible site by site. As a consequence, we figure out an exotic type of supersolid phase which particularly features a dual construction, but in the absence of interactions among different lattice sites. This dual supersolid state could be further supported by solving the Bose–Hubbard model via an exact diagonalization method, and feasibly generalized to a limiting case of hardcore bosons. We also map out the phase diagram with the help of the time-dependent variational Gutzwiller method. And it manifests that the regime of dual supersolid state is dominant. • The Bose–Hubbard model on the Lieb lattice is studied. • We identify the dual supersolid without off-site interaction. • We map out the phase diagram of the bosonic Lieb lattice.
We study the ground-state properties of the extended Bose-Hubbard model in a one-dimensional dimerized optical lattice. In the limit of strong on-site repulsion, i.e., hardcore bosons, and strong nearest-neighbor interaction, a stable density-wave (DW) phase is obtained at half-filling as a function of lattice dimerization. Interestingly, at quarter-filling we obtain the signatures of an insulating phase which has the character of both the bond order (BO) and the DW insulators, which we call a bond-order density-wave (BODW) phase. Moreover, we show that for a fixed hopping dimerization there occurs a BO-DW phase crossover as a function of the nearest-neighbor interaction and the BODW phase is more robust when the hopping dimerization is stronger. We further examine the stability of the BODW phase in the limit of finite on-site interactions.
Abstract The effect of many-body interaction in curved space is studied based on the extended Bose–Hubbard model on hyperbolic lattices. Using the mean-field approximation and quantum Monte Carlo simulation, the phase diagram is explicitly mapped out, which contains the superfluid, supersolid and insulator phases at various fillings. Particularly, it is revealed that the sizes of the Mott lobes shrink and the supersolid is stabilized at smaller nearest-neighbor interaction as q in the Schläfli symbol increases. The underlying physical mechanism is attributed to the increase of the coordination number, and hence the kinetic energy and the nearest-neighbor interaction. The results suggest that the hyperbolic lattices may be a unique platform to study the effect of the coordination number on quantum phase transitions, which may be relevant to the experiments of ultracold atoms in optical lattices.
We investigate the phase diagram of a one-dimensional model of hardcore bosons or spinless fermions with tunable nearest-neighbor interactions. By introducing alternating repulsive and attractive interactions on consecutive bonds, we show that the system undergoes a transition from a bond-ordered (BO) phase to a charge-density wave-II (CDW-II) phase as the attractive interaction strength increases at a fixed repulsive interaction. For a specific interaction pattern, the BO phase exhibits topological properties, which vanish when the pattern is altered, leading to a transition from a topological BO phase to a trivial BO phase through a gap-closing point where both interactions vanish. We identify these phases using a combination of order parameters, topological invariants, edge-state analysis and Thouless charge pumping. By extending our analysis beyond half-filling, we explore the phase diagram across all densities and identify the superfluid (SF) and the pair-superfluid (PSF) phases, characterized by single-particle and bound-pair excitations at incommensurate densities. The proposed model is experimentally realizable in platforms such as Rydberg excited or ultracold atoms in optical lattices, offering a versatile framework to study such interplay between topology and interactions in low-dimensional systems.
We consider a minimal model to investigate the quantum phases of hardcore, polarized dipolar atoms confined in multilayer optical lattices. The model is a variant of the extended Bose-Hubbard model, which incorporates intralayer repulsion and interlayer attraction between the atoms in nearest-neighbor sites. We study the phases of this model emerging from the competition between the attractive interlayer interaction and the interlayer hopping. Our results from the analytical and cluster-Gutzwiller mean-field theories reveal that multimer formation occurs in the regime of weak intra- and interlayer hopping due to the attractive interaction. In addition, intralayer isotropic repulsive interaction results in the checkerboard ordering of the multimers. This leads to an incompressible checkerboard multimer phase at half-filling. At higher interlayer hopping, the multimers are destabilized to form resonating valence-bond-like states. Furthermore, we discuss the effects of thermal fluctuations on the quantum phases of the system.