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arXiv:2605.06171 · Physical Review A

Quantum phase diagrams for bosons in hexagonal optical potentials: A continuous-space quantum Monte Carlo study

Danilo Nascimento Guimaraes, Laurent Sanchez-Palencia

cond-mat.quant-gasquant-phSubmitted May 7, 2026• Announced May 8, 2026• 0 citations• Revised Jul 21, 2026 (v2)
v1 · May 7, 2026v2 · Jul 21, 2026
arXivHTMLPDF

Abstract

Hexagonal optical lattices, emulating graphene and hexagonal boron nitride (h-BN) structures, provide a versatile platform for exploring strongly correlated quantum matter. Using continuous-space exact diagonalization and quantum Monte Carlo simulations, we investigate the phase diagrams of ultracold bosons in honeycomb and h-BN lattices. For the honeycomb lattice, we find significant deviations from the standard Bose--Hubbard model even for strong lattice amplitudes. We observe suppressed Mott insulator lobes and the absence of higher-order insulating phases, which we attribute to strong density-assisted tunneling effects. In the h-BN case, a rich phase diagram emerges, featuring multiple Mott lobes with various sublattice occupations, driven by the interplay of lattice asymmetry, interactions, and particle filling. Our results highlight the necessity of continuous-space treatments for capturing the full complexity of bosonic quantum phases in hexagonal geometries, paving the way for experimental realizations with ultracold atoms and further theoretical work.

Journal reference
Phys. Rev. A 114, 023312 (2026)
DOI
10.1103/k9ym-r23v

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