Ground states of quantum XY dipoles on the Archimedean lattices

TL;DR

This paper uses large-scale numerical simulations to explore the ground states of the dipolar XY spin model on various Archimedean lattices, revealing diverse magnetic and quantum phases.

Contribution

It provides the first comprehensive numerical analysis of the dipolar XY model on nine Archimedean lattices, identifying different ordered and disordered phases.

Findings

Four lattices host trivial paramagnets.

Four lattices develop collinear Neel order.

Triangular lattice exhibits competing phases including spin liquid.

Abstract

We report numerical ground states for the dipolar XY spin model, which describes extended antiferromagnetic interactions in two-dimensional arrays of polar molecules and two-level Rydberg atoms. Carrying out large-scale density matrix renormalization group (DMRG) calculations, we compute ground state properties on nine of the eleven Archimedean lattices--tilings of the plane by regular polygons. Four of these host trivial paramagnets, while another four develop collinear Neel magnetic order, as was found previously for the square lattice. For the ordered states, we calculate the hydrodynamic parameters (magnetization, susceptibility, and stiffness) and compare to linear spin wave theory. We also investigate the triangular lattice, for which we find several competing phases including coplanar magnetism, stripe density wave order, and a possible spin liquid; their relative stability is sensitive to the long-range couplings present in our dipolar model. Finally, the Archimedean classification is completed by the kagome lattice, which we argue in a companion work is likely to be a Dirac spin liquid.