Systematic Analysis of Crystalline Phases in Bosonic Lattice Models with Algebraically Decaying Density-Density Interactions

TL;DR

This paper introduces a systematic method to analyze crystalline phases in bosonic lattice models with long-range interactions, applying it to various models and lattice geometries to identify ground states and phase structures.

Contribution

The authors develop a general framework for analyzing crystalline phases in bosonic lattice models with algebraically decaying interactions, applicable to arbitrary lattices and interaction ranges.

Findings

Identified a six-fold degenerate stripe phase as the ground state for the antiferromagnetic Ising model on the triangular lattice.

Applied the method to Rydberg atom arrays on Kagome lattices, revealing stable crystalline arrangements.

Provided a versatile approach for studying long-range interaction effects on crystalline order.

Abstract

We propose a general approach to analyse diagonal ordering patterns in bosonic lattice models with algebraically decaying density-density interactions on arbitrary lattices. The key idea is a systematic search for the energetically best order on all unit cells of the lattice up to a given extent. Using resummed couplings we evaluate the energy of the ordering patterns in the thermodynamic limit using finite unit cells. We apply the proposed approach to the atomic limit of the extended Bose-Hubbard model on the triangular lattice at fillings $f=1/2$ and $f=1$. We investigate the ground-state properties of the antiferromagnetic long-range Ising model on the triangular lattice and determine a six-fold degenerate plain-stripe phase to be the ground state for finite decay exponents. We also probe the classical limit of the Fendley-Sengupta-Sachdev model describing Rydberg atom arrays. We focus on arrangements where the atoms are placed on the sites or links of the Kagome lattice. \changed{Our method provides a general framework to treat cristalline structures resulting from long-range interactions.