Detecting the critical point through entanglement in the Schwinger model

Using quantum simulations on classical hardware, we study the phase diagram of the massive Schwinger model with a θ term at finite chemical potential μ. We find that the quantum critical point in the phase diagram of the model can be detected through the entanglement entropy and entanglement spectrum. As a first step, we chart the phase diagram using conventional methods by computing the dependence of the charge and chiral condensates on the fermion mass m, coupling constant g, and the chemical potential μ. At zero density, the Schwinger model possesses a quantum critical point at θ=π and m/g≃0.33. We find that the position of this quantum critical point depends on the chemical potential. Near this quantum critical point, we observe a sharp maximum in the entanglement entropy. Moreover, we find that the quantum critical point can be located from the entanglement spectrum by detecting the position of the gap closing point.