Preparation of a Quantum Spin Liquid in Non-Hermitian Quantum Dimer Models and Rydberg Arrays

Abstract

We identify an unconventional form of the non-Hermitian skin effect that occurs not in position space but in many-body Fock space, which we call the Fock space skin effect (FSSE). Using quantum dimer models, we characterize FSSE analytically and numerically, and propose a concrete route toward its realization in Rydberg atom arrays. The dimer constraint is enforced through Rydberg gadgets employing the blockade mechanism, while directional reservoirs generate non-Hermitian flipping amplitudes. We show that FSSE enables the preparation of gapped spin liquid states, and in particular, we demonstrate how a Rydberg geometry realizing a square lattice quantum dimer model with next-nearest neighbor dimers can be driven by non-Hermiticity into an exact spin liquid ground state. Our results establish Fock-space non-Hermiticity as a powerful principle for engineering exotic quantum phases and dynamical state-preparation protocols.