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.

Figures (3)

• Figure 1: (a) and (b) show examples of close-packed dimer coverings on ladder and square lattice geometries. (c) and (d) show examples of columnar configurations in the ladder and square lattice geometries, respectively. (e) pictorially shows the nonreciprocal flipping amplitudes in the kinetic term of the non-Hermitian QDM (Eq. \ref{['eq:T_NH']}).
• Figure 2: (a) shows the mapping between dimer configurations (left side of identities) to hardcore bosons living on the links of the lattice (right side of identities). (b) shows the columnar asymmetry, as defined in the main text, of the ground state $\ket{\psi_0(V,\gamma)}$ for the square lattice (system size: $6\times 6$). (c) shows the columnar overlaps of the ground state $\ket{\psi_0(V=t,\gamma)}$ (in the (0,0) winding number sector) for the ladder geometry (system size: $16\times 2$). The blue (orange) curve in (c) corresponds to the overlap of $\ket{\psi_0}$ with the columnar state $\ket{\Phi^h}$ ($\ket{\Phi^v}$) with horizontal (vertical) dimers. (d) shows the average quadrupole moment $\langle Q_{xx} - Q_{yy} \rangle$ in the ground state $\ket{\psi_0(V,\gamma)}$ for the square lattice geometry. (e) shows the asymmetry between horizontal and vertical dimers in the ladder geometry. The asymmetry is non-vanishing even for $\gamma=0$ because the ladder model lacks $C_4$ rotation symmetry. Finite $\gamma$ can tune the asymmetry back to a vanishing point.
• Figure 3: Rydberg atom geometries for quantum dimer models. (a) shows the geometry optimal for the realization of the QDM on a square lattice. The link atoms (blue) are of the same species as the gadget atoms (red). The lattice spacing is taken such that each link atom blockades six gadget atoms, as shown. Here $R'_b$ is the radius of the extended interaction range. (b) shows the Rydberg-atom configuration that achieves the Yao-Kivelson model. This geometry includes interstitial atoms (green) that encode NNN dimers. Here $R_{bI}$ is the blockade radius and $R'_{bI}$ is the radius of the extended interaction range of the interstitial atoms. (c) shows a valid dimer covering in the ladder geometry. Each dimer comprises an active link atom and two active gadget atoms. The same holds for the square lattice geometry as well. We couple the link atoms only on the horizontal links (or equivalently, vertical links) to directional reservoirs to achieve non-Hermitian couplings in the plaquette-flip term of the effective Hamiltonian. (d) illustrates that two active interstitial atoms on a diagonal encode an NNN dimer on that diagonal. We couple the interstitial atoms to directional reservoirs to achieve the non-Hermitian flipping term in Eq. \ref{['eq:T2NH']}. The blue and red wavy arrows represent the new amplitudes of the $\ket{\text{Gnd}}\bra{\text{Ryd}}$ and $\ket{\text{Ryd}}\bra{\text{Gnd}}$ of the interstitial atoms, respectively.