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

TL;DR

This study uses continuous-space quantum Monte Carlo simulations to explore the complex phase diagrams of ultracold bosons in hexagonal optical lattices, revealing deviations from simplified models and rich phase structures.

Contribution

It provides the first detailed continuous-space analysis of bosonic phases in honeycomb and h-BN lattices, highlighting effects beyond the Bose-Hubbard model.

Findings

Significant deviations from the Bose-Hubbard model in honeycomb lattices.

Suppressed Mott lobes and absence of higher-order insulating phases.

Rich phase diagram with multiple Mott lobes in h-BN lattices.

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.