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arXiv:2504.19837 · Journal of Physics Condensed Matter

Thermal melting of incompressible phases in pure and disordered extended Bose–Hubbard models

Madhumita Kabiraj, Raka Dasgupta

Published Jan 30, 2026• 1 citation
arXivHTMLPDF

Abstract

We investigate the thermal melting of the incompressible lobes in the extended Bose-Hubbard model for both pure and disordered systems, motivated by recent experimental realizations using ultracold Rydberg atoms in optical lattices. By tuning the Rydberg excitation level and the lattice spacing, one can engineer the system to effectively have (i) only the nearest-neighbor (NN) interaction or (ii) NN and next-NN interactions. For both these schemes, we employ a mean-field framework to map out the finite-temperature phase diagrams. It is observed that the conventional Mott-insulating and density-wave lobes gradually transform into a normal fluid with increasing temperature. The melting temperature of the Mott lobes is controlled by the on-site interaction, while that of the density-wave lobes is governed by its NN counterpart. We also observe that the inclusion of disorder lowers the melting temperatures of both these insulating phases. The additional Bose-glass phase that appears in the presence of disorder, however, does not vanish at higher temperatures. Instead, it starts occupying a larger area in the phase diagram. The formalism that we present here is capable of treating long-range interactions, disorder, and finite temperature all at once. Moreover, it is versatile enough so that it can be extended to study other forms of disorder, and also be tailored to include longer-range interactions.

DOI
10.1088/1361-648x/ae3ffc

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The introduction of disorder in the extended Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass and disordered solid phases. In this work, we present a rich phase diagram of interacting bosons in a disordered two-dimensional optical lattice, modeled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean-field theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the disordered solid and Bose-glass phases. We have investigated this transition in greater detail using cluster Gutzwiller mean-field theory to study the effect of intersite correlations which is absent in the single-site Gutzwiller mean-field theory. We have also studied this phase transition from the perspective of percolation theory.
By using the inhomogeneous mean-field theory, the phase diagram of the two-dimensional soft-core extended Bose-Hubbard model with both on-site and nearest-neighbor interactions in the presence of spatial disorder is determined. Rich phases, including Mott-insulator, checkerboard solid, supersolid, superfluid and disordered solid are obtained. Interestingly, due to the presence of disorder, a new disordered solid phase is found between the incompressible lobes, and it is demonstrated that the supersolid phase can survive in two-dimensional soft-core bosons. Furthermore, the system undergoes the phase transition from a disordered solid into a solid order or supersolid landscape when the disorder strength is increased. For weak nearest-neighbor repulsion, the increase of the disorder strength induces both checkerboard solid and supersolid phases shrinking to smaller hopping regions. However, for strong nearest-neighbor repulsion, the disorder stabilizes the supersolid phase and makes it occupying a remarkably broad region in the phase diagram. The analytical expressions for the phase boundaries between the incompressible and compressible phases are also obtained, which are in qualitative agreement with our numerical results.
For systems of interacting, ultracold spin-zero neutral bosonic atoms, harmonically trapped and subject to an optical lattice potential, we derive an Extended Bose Hubbard (EBH) model by developing a systematic expansion for the Hamiltonian of the system in powers of the lattice parameters and of a scale parameter, the lattice attenuation factor. We identify the dominant terms that need to be retained in realistic experimental conditions, up to nearest-neighbor interactions and nearest-neighbor hoppings conditioned by the on-site occupation numbers. In the mean field approximation, we determine the free energy of the system and study the phase diagram both at zero and at finite temperature. At variance with the standard on site Bose Hubbard model, the zero-temperature phase diagram of the EBH model possesses a dual structure in the Mott insulating regime. Namely, for specific ranges of the lattice parameters, a density wave phase characterizes the system at integer fillings, with domains of alternating mean occupation numbers that are the atomic counterparts of the domains of staggered magnetizations in an antiferromagnetic phase. We show as well that in the EBH model, a zero-temperature quantum phase transition to pair superfluidity is, in principle, possible, but completely suppressed at the lowest order in the lattice attenuation factor. Finally, we determine the possible occurrence of the different phases as a function of the experimentally controllable lattice parameters.
The introduction of disorder in Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass (BG) and disordered solid (DS) phases. In this work, we present the rich phase diagram of interacting bosons in disordered two-dimensional optical lattice, modelled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean field (SGMF) theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the DS and BG phases. We have investigated this transition in greater detail using cluster Gutzwiller mean field theory to study the effect of inter-site correlations which is absent in the SGMF method. We have also studied this phase transition from the perspective of percolation theory.
We address the phase diagram of the disordered Bose-Hubbard model that has been realized in several recent experiments in terms of optically trapped ultracold bosons. We show that a systematic description of all of the expected quantum phases can be obtained at both zero and finite temperature via a site-dependent decoupling mean-field approach. Also, we relate the boundaries of the Mott-insulating phase to an off-diagonal noninteracting Anderson model whose spectral features provide an avenue for determining the debated nature of the phase surrounding the Mott lobes. Our approach is simple yet effective, and scalable to systems with experimentally relevant sizes and features.