Quantum Spin Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics*

Abstract: Ground states of many-body quantum systems can potentially host long-ranged entangled states known as quantum spin liquids (QSLs). The requirements for realizing such equilibrium states are rather demanding, including strong quantum resonances in the Hamiltonian and the ability to cool below the energy gap. Here, we show how non-equilibrium dynamics can provide a more streamlined route toward creating QSLs. By first focusing on the simplest $mathbb{Z}_2$ toric code spin liquid, with gapped charge and flux excitations, we outline a dynamical protocol that begins in the short-range entangled ``Higgs'' phase and proceeds to sweep parameters to remove the condensed charge excitations. When there is a separation of scales between the motion of charge ($e$-anyons) and flux ($m$-anyons) excitations, we identify a dynamical regime in which the sweep is quasi-adiabatic with respect to the charge but sudden with respect to flux. Targeting this regime we demonstrate robust preparation of the spin liquid state in finite-sized regions, which we brand ``quantum spin lakes''. This mechanism sheds light on recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. We conclude by highlighting two striking consequences of our theory. First, we emphasize that paradoxically, the absence---rather than presence---of quantum resonances aid in stabilizing the dynamical preparation of quantum spin liquids. This leads us to recognize that the dynamics observed experimentally and in full-scale numerics are well approximated by tree tensor network simulations of tree lattices. Finally, we highlight that even spin liquid states that are unstable in equilibrium---namely, $2 + 1$D $U(1)$ spin liquid states---can be stably prepared by non-equilibrium dynamics.