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arXiv:2605.07685

Ground states of quantum XY dipoles on the Archimedean lattices

Marcus Bintz, Ahmed Khalifa, Vincent S. Liu, Johannes Hauschild, Michael P. Zaletel, Shubhayu Chatterjee, Norman Y. Yao

Published May 8, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2605.07685

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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.
This thesis demonstrates that arrays of electric dipoles are good analogs for quantum magnets. We center our investigation on a recently developed experiment, in which rubidium-87 atoms are trapped in optical tweezers and then excited into two distinct electronic Rydberg states. The electric dipole-dipole interaction between these Rydberg atoms is mathematically modeled by a spin Hamiltonian with easy-plane anisotropy, and coupling strength decaying as the inverse cube of the distance. We approximately solve for the ground state of this model Hamiltonian on each of the eleven Archimedean lattices, through large-scale density matrix renormalization group calculations. For the kagome lattice, we gather extensive numerical evidence for an emergent quantum spin liquid, similar to that occurring in the canonical Heisenberg model of quantum magnetism. We predict this spin liquid to be of 𝑈(1) Dirac type, and propose new protocols for experimentally preparing and characterizing it. Our theoretical calculations support the collaborative design and analysis of experiments studying dipolar Rydberg atoms in square, circular, and kagome arrays. These respectively result in observations of continuous symmetry breaking, Tomonaga-Luttinger liquid behavior, and an atomic spin liquid candidate.
We predict that the gapless U(1)U(1)U(1) Dirac spin liquid naturally emerges in a two-dimensional array of quantum dipoles. In particular, we demonstrate that the dipolar XY model$\unicode{x2014}$realized in both Rydberg atom arrays and ultracold polar molecules$\unicode{x2014}$hosts a quantum spin liquid ground state on the kagome lattice. Large-scale density matrix renormalization group calculations indicate that this spin liquid exhibits signatures of gapless, linearly-dispersing spinons, consistent with the U(1)U(1)U(1) Dirac spin liquid. We identify a route to adiabatic preparation via staggered on-site fields and demonstrate that this approach can prepare cold spin liquids within experimentally realistic time-scales. Finally, we propose a number of novel signatures of the Dirac spin liquid tailored to near-term quantum simulators, including termination-dependent edge modes and the Friedel response to a local perturbation.
Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1/2 dipolar Heisenberg model with competing anisotropic, long-range exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the J_{1}-J_{2} model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The ground state phase diagrams obtained from Schwinger-boson and spin-wave theories consistently show a spin disordered region between the Néel, stripe, and spiral phase. The existence of a finite quantum paramagnetic region is further confirmed by an unbiased variational ansatz based on tensor network states and a tensor renormalization group.
Despite long-standing theoretical interest, the chiral spin liquid, a topologically ordered phase, has yet to be observed experimentally. Here we surprisingly find its emergence in an experimentally realized dipolar XY\text{XY}XY model when Rydberg atoms are arranged in a breathing kagome lattice. Using the infinite density matrix renormalization group, we numerically calculate the ground state's chiral order parameter, spin-spin correlations, Chern number, and entanglement spectrum. Our numerical results provide strong evidence for the chiral spin liquid phase. Furthermore, we identify a quantum phase transition from a Dirac spin liquid to a chiral spin liquid as the lattice geometry is tuned from the isotropic kagome to the breathing kagome lattice.
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