Dirac Spin Liquid Candidate in a Rydberg Quantum Simulator

Abstract

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.

Figures (11)

• Figure 1: Dipolar XY model on a kagome array. (a) Fluorescence image of $N = 114~$individual $^{87}\text{Rb}~$atoms trapped in a kagome array of optical tweezers (dotted lines emphasizing the kagome structure are guides to the eye). The lattice spacing is $a = 12\,\mu$m. (b) Schematic depicting the dipolar XY model. The spin states are encoded in a pair of Rydberg states which exhibit dipolar spin-exchange interactions. We denote $A$ the sub-array of the addressed atoms whose $\ket{\uparrow}$ state is lightshifted by $\delta$ and $B$ the sub-array of the non-addressed atoms.
• Figure 2: Adiabatic preparation of the ground state. (a) Average staggered $z$-magnetization $P_z$ as a function of $|\delta / J|$. (b) Evolution of the entanglement witness $\xi^2$ (see text) as a function of $|\delta/J|$. (c) Average nearest-neighbor connected correlations measured along $z$ (circle markers) and $x$ (square markers) as a function of $|\delta / J|$. To avoid edge effects, the purple and light blue data show the average calculated using only the purple and light blue nearest-neighbor pairs shown in the inset. We identify three phases: the staggered state, the pinned crystal phase and the correlated liquid phase. The background colors are a guide to the eye to represent these different phases. (d-f) For each phase ($|\delta / J| = [13.0,1.16,0.0025]$), we represent the $z$ magnetization $\langle \sigma^z_i \rangle$ of each atom (colored circles) and the connected nearest-neighbor and next-nearest-neighbor correlations $\langle \sigma^z_i\sigma^z_j \rangle_c$ (colored bonds). In the staggered initial state, the atoms with a positive magnetization belong to the sub-array $A$, and the others belong to $B$. (g) Momentum-space structure factor of the correlated liquid in the $\sigma^z$ (top) and $\sigma^x$ (bottom) bases. The dashed and dash-dot line represent the extended Brillouin and regular Brillouin zone supp. (h) Four-body bond-bond correlations (see text).
• Figure 3: Thermometry. (a) Staggered magnetization dynamics during a mirrored forward-then-backward ramp. (b) Calibration curve of thermodynamic entropy as a function of temperature for the kagome Heisenberg antiferromagnet, adapted from Ref. schnackMagnetism42Kagome2018. (c) Spin structure factor following a rapid quench to a high-temperature state. (d) Nearest-neighbor $\sigma^z$ correlations for varying ramp times $\tau$.
• Figure 4: Liquid correlations. (a) Spin structure factor in the experimentally prepared liquid (top) and theoretical Gutzwiller ansatz (bottom). (b) Modified structure factor, with the nearest-neighbor correlations subtracted off. (c) Map of correlation function $C^{xx}_{\mathbf{d} = (d_x,d_y)}$. (d) Spatial decay of correlations, comparing the experiment (solid circles) to the Gutzwiller ansatz (light squares). We average over pairs $(i,j)$ where $i$ is in the center 42 sites (inset) and $j$ is anywhere in the array. Blue markers indicate $C^x_d<0$, red markers indicate $C^x_d>0$, and gray markers are data within statistical error of zero. The results of fits are the following: $\alpha_{\rm GA} = -3.5 \pm 0.7$, $\alpha_{\rm Exp} = -4.0 \pm 1.0$, $\zeta_{\rm GA}/a = 0.33 \pm 0.03$ and $\zeta_{\rm Exp}/a= 0.34 \pm 0.02$.
• Figure 5: Static susceptibilites. (a) Change in magnetization $\Delta \langle \sigma^z_r\rangle = \langle \sigma^z_r\rangle(\delta_{\rm{loc}}) - \langle \sigma^z_r\rangle(\delta_{\rm{loc}} = 0)$ induced by a single-site field, $\delta_{\rm{loc}} \sigma^z_0$ as a function $\delta$, averaged over sites at distance $r$ from the targeted atom. (b) Local map of the experimentally measured susceptibility. The position of the atom addressed with the local addressing beam is indicated by a slightly larger circle. (c) Theoretical expectation from Gutzwiller ansatz. (d) Change in correlations $\Delta C^{xx}$ due to lattice distortion. Bonds shortened by 5% are thickened. (e) Histogram of distortion response on nearest-neighbor bonds.