Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model

We present an Ansatz for the ground states of the quantum Sherrington-Kirkpatrick model, a paradigmatic model for quantum spin glasses. Our Ansatz, based on the concept of generalized coherent states, very well captures the fundamental aspects of the model, including the ground state energy and the position of the spin glass phase transition. It further enables us to study some previously unexplored features, such as the nonvanishing longitudinal field regime and the entanglement structure of the ground states. We find that the ground state entanglement can be captured by a simple ensemble of weighted graph states with normally distributed phase gates, leading to a volume law entanglement, contrasting with predictions based on entanglement monogamy.