Abstract:
Rydberg tweezer arrays provide a versatile platform to explore quantum magnets. Different types of interactions, such as dipolar $\sigma^+ \sigma^-$ (XY), van-der-Waals Ising $\sigma^z \sigma^z$ (ZZ), and spin-flip $\sigma^x$ terms, can simultaneously exist.
Furthermore, the Rydberg blockade mechanism can prevent the excitation of another, nearby-situated Rydberg atom akin to the Gauss law in lattice gauge theory.
In the talk I report on two different types of physics that can be realized with such platforms.
First, I comment on a recent experiment which exploited the blockade mechanism in order to observe the onset of a dynamically prepared, gapped $Z_2$ quantum spin liquid on the ruby lattice (Semgehini et al, Science 374, 1242 (2021)). 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 {\it 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 $\delta$ and starting from $T/\Omega \sim 0.5$ (in units of the Rabi frequency $\Omega$) down to the lowest temperatures we could simulate, $T/\Omega \sim 0.01$. With Van der Waals ZZ interactions, constant entropy plateaus are still found but their value shifts with $\delta$. I comment on the adiabatic approximation to the dynamical ramps for the electric degrees of freedom, and the magnitude of the observed string parity order parameters.
Second, through combining the dipolar XY and Ising ZZ interactions, we predict the existence of a robust supersolid phase on the triangular lattice based on explicitly calculated pair interactions for $^{87}Rb$ and with a critical entropy per particle $S/N \approx 0.19$. Such a lattice supersolid is long-lived, found over a wide parameter range in an isotropic and flat two-dimensional geometry, and can be realized with existing technology for 100s of particles. It has true long-range order, even at finite temperature.