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Results in Physics

The supersolidity in a bosonic Lieb lattice

Dian-Cheng Zhang, Changwei Li

Published Oct 28, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1016/j.rinp.2025.108488

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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 studied all possible ground states, including supersolid (SS) phases and phase separations of hard-core- and soft-core-extended Bose-Hubbard models with fixed boson densities by using the Gutzwiller variational wave function and the linear programming method. We found that the phase diagram of the soft-core model depends strongly on its transfer integral. Furthermore, for a large transfer integral, we showed that an SS phase can be the ground state even below or at half filling against the phase separation. We also found that the density difference between nearest-neighbor sites, which indicates the density order of the SS phase, depends strongly on the boson density and transfer integral.
Abstract We theoretically investigate the extended Bose–Hubbard model using a three-dimensional cubic lattice. In the framework of the dynamical Gutzwiller mean-field theory, we identify a checkerboard supersolid phase. By considering the repulsive interactions between next-nearest-neighbor lattice sites, we further discover an exotic type of supersolid state, whose site occupancies show a stereoscopically arrayed and staggered distribution rather than checkerboard ordering. Intriguingly, if the physical observations of two neighboring layers were superimposed, they would give rise to a checkerboard configuration. This novel structure is convincingly induced by the simultaneous existence of nearest-neighbor and next-nearest-neighbor interactions. We also identify arrayed stripes in the ground state, as well as arrayed holes in the pattern of occupancies.
Hard-core and soft-core extended Bose-Hubbard models with fixed boson densities are studied by using the Gutzwiller variational wave function. The phase diagram of the softcore model strongly depends on its transfer integral. Specifically, a supersolid phase can be the ground state even below half-filling for a large transfer integral. The density difference between nearest-neighbor sites, which is an order parameter of the supersolid phase, strongly depends on the boson density, especially for a small transfer integral.
We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (UUU) and nearest-neighbor (VVV) repulsions. For ddd-dimensional hypercubic lattices, when 2dV<U2\mathit{dV}<U2dV<U, it is well known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when 2dV>U2\mathit{dV}>U2dV>U, in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when $2\mathit{dV}\ensuremath{\gtrsim}1.5U$, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.
We study the quantum ground state of ultracold bosons in a two-dimensional square lattice. The bosons interact via the repulsive dipolar interactions and sss-wave scattering. The dynamics is described by the extended Bose-Hubbard model including correlated hopping due to the dipolar interactions, and the coefficients are found from the second quantized Hamiltonian using the Wannier expansion with realistic parameters. We determine the phase diagram using the Gutzwiller ansatz in the regime where the coefficients of the correlated hopping terms are negative and can interfere with the tunneling due to single-particle effects. We show that this interference gives rise to staggered superfluid and supersolid phases at vanishing kinetic energy, while we identify parameter regions at finite kinetic energy where the phases are incompressible. We compare the results with the phase diagram obtained with the cluster Gutzwiller approach and with the results found in one dimension using the density-matrix renormalization group.
We investigate the ground-state phase diagram of the soft-core Bose-Hubbard model with the nearest-neighbor repulsion on a square lattice by using an unbiased quantum Monte Carlo method. In contrast to a previous study [P. Sengupta et al., Phys. Rev. Lett. 94, 207202 (2005)], we present the ground-state phase diagrams up to high hopping amplitudes. As a result, in addition to the known supersolid above half-filling, we find a supersolid phase below and at half-filling for high hopping amplitudes. In addition, for a strong nearest-neighbor repulsion, we show that the supersolid phase occupies a remarkably broad region in the phase diagram. These results are in agreement with the results of the Gutzwiller mean-field approximation [M. Iskin, Phys. Rev. A 83, 051606(R) (2011); T. Kimura, Phys. Rev. A 84, 063630 (2011)]. However, it turns out that the regions of the supersolid phases are significantly smaller than the mean-field results.