Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits

The authors explore critical properties of entanglement phase transitions in random tensor networks and monitored quantum circuits with Clifford tensors/gates for on-site Hilbert space dimensions which are powers of a prime number p. Exact mappings to replica spin models and characterizations of their symmetry groups predict that all universal properties will depend only on p. These predictions are confirmed with extensive numerical simulations. The authors also establish multifractal scaling of the purity, reflected in a continuous spectrum of critical exponents, while the typical exponent is the prefactor of the logarithm in the entanglement entropy.