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arXiv:2406.07110 · Physical Review Letters

Renormalized Classical Spin Liquid on the Ruby Lattice

Z. D. Wang, Lode Pollet

Published Feb 27, 2025• 11 citations
arXivHTMLPDF

Abstract

The recent experimental detection of the onset of a dynamically prepared, gapped Z_{2} quantum spin liquid on the ruby lattice brought the physics of frustrated magnetism and lattice gauge theory to Rydberg tweezer arrays [Semeghini et al., Probing topological spin liquids on a programmable quantum simulator, Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794]. The thermodynamic properties of such models remain inadequately addressed, yet knowledge thereof is indispensable if one wants to prepare large, robust, and long-lived quantum spin liquids. Using large scale quantum Monte Carlo simulations we find in the PXP model a renormalized classical spin liquid with constant entropy density S/N approaching ln(2)/6 in the thermodynamic limit for all moderate and large values of the detuning δ and starting from T/Ω∼0.5 (in units of the Rabi frequency Ω) down to the lowest temperatures we could simulate, T/Ω∼0.01. With van der Waals interactions, constant entropy plateaus are still found but its value shifts with δ. We comment on the implications of the adiabatic approximation to the dynamical ramps for the electric degrees of freedom, which leads to a reinterpretation of the experimental observations.

DOI
10.1103/physrevlett.134.086601

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The recent experimental detection of the onset of a dynamically prepared, gapped Z_{2} quantum spin liquid on the ruby lattice brought the physics of frustrated magnetism and lattice gauge theory to Rydberg tweezer arrays [Semeghini et al., Probing topological spin liquids on a programmable quantum simulator, Science 374, 1242 (2021)SCIEAS0036-807510.1126/science.abi8794]. The thermodynamic properties of such models remain inadequately addressed, yet knowledge thereof is indispensable if one wants to prepare large, robust, and long-lived quantum spin liquids. Using large scale quantum Monte Carlo simulations we find in the PXP model a renormalized classical spin liquid with constant entropy density S/N approaching ln(2)/6 in the thermodynamic limit for all moderate and large values of the detuning δ and starting from T/Ω∼0.5 (in units of the Rabi frequency Ω) down to the lowest temperatures we could simulate, T/Ω∼0.01. With van der Waals interactions, constant entropy plateaus are still found but its value shifts with δ. We comment on the implications of the adiabatic approximation to the dynamical ramps for the electric degrees of freedom, which leads to a reinterpretation of the experimental observations.
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The physical realization of Z 2 topological order as encountered in the paradigmatic toric code has proven to be an elusive goal.We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms placed on the ruby lattice, at specific values of the Rydberg blockade radius.First, we show that the blockade model-also known as a "PXP" model-realizes a monomer-dimer model on the kagome lattice with a single-site kinetic term.This model can be interpreted as a Z 2 gauge theory whose dynamics is generated by monomer fluctuations.We obtain its phase diagram using the numerical density matrix renormalization group method and find a topological quantum liquid (TQL) as evidenced by multiple measures including (i) a continuous transition between two featureless phases, (ii) a topological entanglement entropy of ln 2 as measured in various geometries, (iii) degenerate topological ground states, and (iv) the expected modular matrix from ground state overlap.Next, we show that the TQL persists upon including realistic, algebraically decaying van der Waals interactions VðrÞ ∼ 1=r 6 for a choice of lattice parameters.Moreover, we can directly access topological loop operators, including the Fredenhagen-Marcu order parameter.We show how these can be measured experimentally using a dynamic protocol, providing a "smoking gun" experimental signature of the TQL phase.Finally, we show how to trap an emergent anyon and realize different topological boundary conditions, and we discuss the implications for exploring fault-tolerant quantum memories.
Quantum spin liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of Z 2 topological order [G. Semeghini , ], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. In this work, we propose a way to realize a U(1) quantum spin liquid in three spatial dimensions, described by the deconfined phase of U(1) gauge theory in a pyrochlore lattice Rydberg atom array. We study the ground state phase diagram of the proposed Rydberg system as a function of experimentally relevant parameters. Within our calculation, we find that by tuning the Rabi frequency, one can access both the confinement-deconfinement transition driven by a proliferation of “magnetic” monopoles and the Higgs transition driven by a proliferation of “electric” charges of the emergent gauge theory. We suggest experimental probes for distinguishing the deconfined phase from ordered phases. This work serves as a proposal to access a confinement-deconfinement transition in three spatial dimensions on a Rydberg-based quantum simulator.