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

TL;DR

This paper introduces a novel non-Hermitian skin effect in Fock space, demonstrating how it can be used to prepare quantum spin liquid states in Rydberg atom arrays, opening new avenues for engineering exotic quantum phases.

Contribution

It uncovers the Fock space skin effect in many-body systems and proposes a practical method to realize quantum spin liquids using Rydberg arrays with non-Hermitian dynamics.

Findings

Fock space skin effect (FSSE) identified and characterized analytically and numerically.

FSSE enables the preparation of gapped spin liquid states.

Rydberg array setup can realize a quantum dimer model with non-Hermitian driving.

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.