Quantum phase diagrams for bosons in hexagonal optical potentials: A continuous-space quantum Monte Carlo study
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, attributed 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.
Cite
@article{arxiv.2605.06171,
title = {Quantum phase diagrams for bosons in hexagonal optical potentials: A continuous-space quantum Monte Carlo study},
author = {Danilo Nascimento Guimaraes and Laurent Sanchez-Palencia},
journal= {arXiv preprint arXiv:2605.06171},
year = {2026}
}