Squeezing Classical Antiferromagnets into Quantum Spin Liquids via Global Cavity Fluctuations

Abstract

Cavity quantum electrodynamics with atomic ensembles is typically associated with collective spin phenomena, such as superradiance and spin squeezing, in which the atoms evolve collectively as a macroscopic spin ($S\sim N/2$) on the Bloch sphere. Surprisingly, we show that the tendency toward a collective spin description need not imply collective spin phenomena; rather, it can be exploited to generate new forms of strongly correlated quantum matter. The key idea is to use uniform cavity-mediated interactions to energetically project the system into the total-spin singlet sector ($S=0$) - a highly entangled subspace where the physics is governed entirely by cavity fluctuations. Focusing on Rydberg atom arrays coupled to a single-mode cavity, we show that global cavity fluctuations can effectively squeeze classical antiferromagnets into quantum spin liquids, characterized by non-local entanglement, fractionalized excitations, and emergent gauge fields. This work suggests that cavity QED can be a surprising resource for inducing strongly correlated phenomena, which could be explored in the new generation of hybrid tweezer-cavity platforms.

Figures (8)

• Figure 1: Cavity projection into the singlet sector. (a) Schematic of a hybrid tweezer-cavity platform. A delocalized cavity mode (yellow) mediates uniform all-to-all interactions, while Rydberg interactions (green circles) generates competing short-range Ising couplings on a programmable tweezer array. (b) Structure of the many-body spectrum of the TCI model in the strong-cavity limit, which decouples into blocks labeled by total-spin quantum numbers $(S, M)$, with the lowest energy block corresponding to the singlet sector ($0,0$). (c) Examples of singlet coverings within the exponentially large degenerate manifold of ground states of the all-to-all cavity Hamiltonian ($J_{ij}=0$), composed of pairwise spin singlets (blue ellipses) of arbitrary spatial range.
• Figure 1: ED results for the $J_1$–$J_2$ TCI model on the square lattice. (a) Fidelity susceptibility and (b–f) static spin structure factors of the ground state of the TCI model on the square lattice with $N=36$ sites, shown as functions of $J_2/J_1$ and $\bar{\lambda}/J_1$. The Néel and stripe phases exhibit dominant correlations at the ordering wavevectors $\mathbf{Q}=\mathrm{M}$ and $\mathbf{Q}=\mathrm{X}$, respectively. White dots mark the local maxima of the fidelity susceptibility, indicating possible phase boundaries. All calculations were performed in the zero-magnetization sector and within the $\Gamma.A_1$ space-group irrep, and the static structure factors are summed over symmetry-equivalent momentum.
• Figure 2: Heisenberg singlet mapping. Low-energy spectrum of the $J_1$-$J_2$ TCI model (filled circles) on the (a) square lattice ($J_2/J_1 = 0.5$), (b) triangular lattice ($J_2/J_1 = 0.125$), and (c) kagome lattice ($J_2/J_1 = 0$) in the strong-cavity regime ($\lambda/J_1 = 10^3$). Each system contains $N = 24$ spins with periodic boundary conditions, and only the lowest 20 eigenvalues are shown within a few representative symmetry sectors (see Methods). These spectra are compared with the singlet sector of the corresponding $J_1$-$J_2$ Heisenberg models (open circles), which are predicted to host QSLs. In all cases, we observed a clear one-to-one correspondence between all eigenstates.
• Figure 2: ED results for the $J_1$–$J_2$ TCI model on the triangular lattice. (a) Fidelity susceptibility and (b–f) static spin structure factors of the ground state of the TCI model on the triangular lattice with $N=36$ sites, shown as functions of $J_2/J_1$ and $\bar{\lambda}/J_1$. The stripe and $120^\circ$ phases exhibit dominant correlations at the ordering wavevectors $\mathbf{Q}=\mathrm{M}$ and $\mathbf{Q}=\mathrm{K}$, respectively. White dots mark the local maxima of the fidelity susceptibility, indicating possible phase boundaries. All calculations were performed in the zero-magnetization sector and within the $\Gamma.A_1$ space-group irrep, and the static structure factors are summed over symmetry-equivalent momentum.
• Figure 3: Squeezed AFM ansatz. (a) Classical AFM ground states of the $J_1$-$J_2$ Ising model on the square and triangular lattices. Each state can be written as a product of two macroscopic sublattice spins ($A$ and $B$), polarized in opposite directions (b) Squeezed AFM state visualized as correlated noise distributions on a pair of generalized Bloch spheres, where the joint spin operators are $S_\alpha^\pm=S_\alpha^A \pm S_\alpha^B$. (c) Static spin structure factors as functions of the squeezing parameter. Transverse ferromagnetic correlations (blue line) are squeezed, transverse antiferromagnetic correlations (red line) are anti-squeezed, and longitudinal antiferromagnetic correlations (green line) are partially suppressed.