Entanglement Spectra of the quantum hard-square model: Holographic minimal models

We study the entanglement properties of a quantum lattice-gas model for which we can find the exact ground state (of the Rokhsar-Kivelson type). The ground state can be expressed as a superposition of states, each of which is characterized by a particle configuration with nearest-neighbor exclusion. We show that the reduced density matrix of the model on a ladder is intimately related to the transfer matrix of the classical hard-square model. The entanglement spectra of the model on square and triangular ladders are critical when parameters are chosen so that the corresponding classical hard-square models are critical. A detailed analysis reveals that the critical theories for the entanglement Hamiltonians are $c<1$ minimal conformal field theories. We further show that the entanglement Hamiltonian for the triangular ladder is integrable despite the fact that the original quantum lattice-gas model is non-integrable.