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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
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.
We study the one-dimensional Bose-Hubbard model using the density-matrix renormalization group. For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott insulators and charge-density wave phases are determined. We find a direct phase transition between the charge-density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. In this region a single impurity causes the system to be insulating. An even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac conductivity of the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.
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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.
The first reliable analytic calculation of the phase diagram of the bose gas on a d-dimensional lattice with on-site repulsion is presented. In one dimension, the analytic calculation is in excellent agreement with the numerical Monte Carlo results. In higher dimensions, the deviations from the Monte Carlo calculations are larger, but the correct shape of the Mott insulator lobes is still obtained. Explicit expressions for the energy of the Mott and the “defect” phase are given in a strong-coupling expansion. Typeset using REVTEX 1 Strongly interacting quantum systems continue to challenge theoretical physics. Fermionic examples of strong correlations include high temperature superconductors, heavy fermion materials and metal-insulator transitions. The study of these systems has been confined to either numerical simulations which are plagued by finite-size effects (with the notable exception of the infinite-dimensional expansion) or uncontrollable approximations. Similar problems arise in strongly interacting bosonic systems which have attracted a lot of
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