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arXiv:2602.17427 · Physical Review A

Mott-insulating phases of the Bose-Hubbard model on quasi-1D ladder lattices

Lorenzo Carfora, Callum W. Duncan, Stefan Kuhr, Peter Kirton

cond-mat.quant-gasquant-phSubmitted Feb 19, 2026• Announced Feb 20, 2026• 0 citations• Revised Feb 21, 2026 (v2)
v1 · Feb 19, 2026v2 · Feb 21, 2026
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Abstract

We calculate the phase diagram of the Bose-Hubbard model on a half-filled ladder lattice including the effect of finite on-site interactions. This shows that the rung-Mott insulator (RMI) phase persists to finite interaction strength, and we calculate the RMI-superfluid phase boundary in the thermodynamic limit. We show that the phases can still be distinguished using the number and parity variances, which are observables accessible in a quantum-gas microscope. Phases analogous to the RMI were found to exist in other quasi-1D lattice structures, with the lattice connectivity modifying the phase boundaries. This shows that the the presence of these phases is the result of states with one-dimensional structures being mapped onto higher dimensional systems, driven by the reduction of hopping rates along different directions.

Journal reference
Phys. Rev. A 114, 023301 (2026)
DOI
10.1103/wml6-1kc2
Comments
12 pages, 9 figures

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We calculate the phase diagram of the Bose-Hubbard model on a half-filled ladder lattice including the effect of finite on-site interactions. This shows that the rung-Mott insulator (RMI) phase persists to finite interaction strength, and we calculate the RMI-superfluid phase boundary in the thermodynamic limit. We show that the phases can still be distinguished using the number and parity variances, which are observables accessible in a quantum-gas microscope. Phases analogous to the RMI were found to exist in other quasi-1D lattice structures, with the lattice connectivity modifying the phase boundaries. This shows that the the presence of these phases is the result of states with one-dimensional structures being mapped onto higher dimensional systems, driven by the reduction of hopping rates along different directions.
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We investigate the ground-state and finite-temperature phase diagrams of the Bose-Hubbard model on a honeycomb superlattice. The interplay between the superlattice potential depth $\mathrm{\ensuremath{\Delta}}/t$ and the on-site interaction U/tU/tU/t gives rise to three distinct quantum phases at zero temperature: a superfluid phase, a Mott insulator I phase with unit filling on each site, and a Mott insulator II phase characterized by density imbalance---double occupancy on one sublattice and vacancy on the other at unit filling. The SF-MI transitions are found to be continuous, consistent with second-order quantum phase transitions. We further extend our analysis to finite temperatures within the superfluid regime. Our work highlights how a honeycomb superlattice geometry enables access to interaction- and lattice-modulation-driven quantum phases, including a density-imbalanced Mott insulator and a robust superfluid regime, offering concrete theoretical predictions for cold-atom experiments.
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We study phase diagrams of one-dimensional bosons with contact interactions in the presence of a lattice. We use the worm algorithm in continuous space and focus on the incommensurate superfluid--Mott-insulator transition. Our results are compared to those from the one-band Bose-Hubbard model. When Wannier states are used to determine the Bose-Hubbard model parameters, the comparison unveils an apparent breakdown of the one-band description for strong interactions, even for the Mott-insulating state with an average of one particle per site (n=1n=1n=1) in deep lattices. We introduce an inverse confined scattering analysis to obtain the ratio U/JU/JU/J, with which the Bose-Hubbard model provides correct results for strong interactions, deep lattices, and n=1n=1n=1.
We establish the phase diagram of the disordered three-dimensional Bose-Hubbard model at unity filling which has been controversial for many years. The theorem of inclusions, proven by Pollet et al. [Phys. Rev. Lett. 103, 140402 (2009)] states that the Bose-glass phase always intervenes between the Mott insulating and superfluid phases. Here, we note that assumptions on which the theorem is based exclude phase transitions between gapped (Mott insulator) and gapless phases (Bose glass). The apparent paradox is resolved through a unique mechanism: such transitions have to be of the Griffiths type when the vanishing of the gap at the critical point is due to a zero concentration of rare regions where extreme fluctuations of disorder mimic a regular gapless system. An exactly solvable random transverse field Ising model in one dimension is used to illustrate the point. A highly nontrivial overall shape of the phase diagram is revealed with the worm algorithm. The phase diagram features a long superfluid finger at strong disorder and on-site interaction. Moreover, bosonic superfluidity is extremely robust against disorder in a broad range of interaction parameters; it persists in random potentials nearly 50 (!) times larger than the particle half-bandwidth. Finally, we comment on the feasibility of obtaining this phase diagram in cold-atom experiments, which work with trapped systems at finite temperature.
We present a cluster mean-field study for ground-state phase diagram and many-body dynamics of spin-1 bosons confined in a two-chain Bose–Hubbard ladder (BHL). For unbiased BHL, we find superfluid (SF) phase and integer filling Mott insulator (IntMI) phase. For biased BHL, in addition to the SF and IntMI phases, there appears half-integer filling Mott insulator (HIntMI) phase. The phase transition between the SF and IntMI phases can be first order at a part of phase boundaries, while the phase transition between the SF and HIntMI phases is always second order. By tuning the bias energy, we report on the change of the nature of SF–MI phase transitions. Furthermore, we study the effect of the spin-dependent interaction on the many-body population dynamics. The spin-dependent interaction can lead to rich dynamical behaviors, but does not influence the particle transfer efficiency. Our results indicate a way to tune the nature of the SF–MI phase transition and open a new avenue to study the many-body dynamics of spinor bosons in optical lattices.