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.