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arXiv:2603.25784

A Dipolar Chiral Spin Liquid on the Breathed Kagome Lattice

Francisco Machado, Sabrina Chern, Michael P. Zaletel, Norman Y. Yao

cond-mat.quant-gascond-mat.str-elphysics.atom-phquant-phSubmitted Mar 26, 2026• Announced Mar 30, 2026• 0 citations• Revised Jun 19, 2026 (v3)
v1 · Mar 26, 2026v2 · Apr 15, 2026v3 · Jun 19, 2026
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Abstract

Continuous control over lattice geometry, when combined with long-range interactions, offers a powerful yet underexplored tool to generate highly frustrated quantum spin systems. By considering long-range dipolar antiferromagnetic interactions on a breathed Kagome lattice, we demonstrate how these tools can be leveraged to stabilize a chiral spin liquid. We support this prediction with large-scale density-matrix renormalization group calculations and explore the surrounding phase diagram, identifying a route to adiabatic preparation via a locally varying magnetic field. At the same time, we identify the relevant low-energy degrees of freedom in each unit cell, providing a complementary language to study the chiral spin liquid. Finally, we carefully analyze its stability and signatures in finite-sized clusters, proposing direct, experimentally viable measurements of the chiral edge mode in both Rydberg atom and ultracold polar molecule arrays.

Comments
22 + 14 pages, 11 + 9 figures

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Continuous control over lattice geometry, when combined with long-range interactions, offers a powerful yet underexplored tool to generate highly frustrated quantum spin systems. By considering long-range dipolar antiferromagnetic interactions on a breathed Kagome lattice, we demonstrate how these tools can be leveraged to stabilize a chiral spin liquid. We support this prediction with large-scale density-matrix renormalization group calculations and explore the surrounding phase diagram, identifying a route to adiabatic preparation via a locally varying magnetic field. At the same time, we identify the relevant low-energy degrees of freedom in each unit cell, providing a complementary language to study the chiral spin liquid. Finally, we carefully analyze its stability and signatures in finite-sized clusters, proposing direct, experimentally viable measurements of the chiral edge mode in both Rydberg atom and ultracold polar molecule arrays.
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.
We experimentally investigate a frustrated spin-exchange antiferromagnet in a quantum simulator, composed of N = 114 dipolar Rydberg atoms arranged into a kagome array. Motivated by a recent theoretical proposal of a gapless U(1) Dirac spin liquid ground state, we use local addressing to adiabatically prepare low-energy states. We measure the local polarization and spin-spin correlations over this adiabatic protocol, and observe our system move from a staggered product state, through an intermediate magnetic crystal, and finally into a disordered, correlated liquid. We estimate the entropy density of this atomic liquid to be similar to that of frustrated magnetic insulators at liquid nitrogen temperatures. We compare the correlations in our liquid to those of a simple, parameter-free ansatz for the Dirac spin liquid, and find good agreement in the sign structure and spatial decay. Finally, we probe the static susceptibility of our system to a local field perturbation and to a geometrical distortion. Our results establish Rydberg atom arrays as a promising platform for the preparation and microscopic characterization of quantum spin liquid candidates.
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.
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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.
Arrays of Rydberg atoms interacting via dipole-dipole interactions offer a powerful platform for probing quantum many-body physics. However, these intrinsic interactions also determine and constrain the models-and parameter regimes thereof-for quantum simulation. Here, we propose a systematic framework to engineer arbitrary desired long-range interactions in Rydberg-atom lattices, enabling the realization of fully tunable J_{1}-J_{2}-J_{3} Heisenberg models. Using site-resolved periodic modulation of Rydberg states, we develop an experimentally feasible protocol to precisely control the interaction ratios J_{2}/J_{1} and J_{3}/J_{1} in a kagome lattice. This control can increase the effective range of interactions and drive transitions between competing spin-ordered and spin-liquid phases. To generalize this approach beyond the kagome lattice, we reformulate the design of modulation patterns through a graph-theoretic approach, demonstrating the universality of our method across all 11 planar Archimedean lattices. Our strategy overcomes the inherent constraints of power-law-decaying dipolar interactions, providing a versatile toolbox for exploring frustrated magnetism, emergent topological phases, and quantum correlations in systems with long-range interactions.