Emergent conformal symmetry in non-unitary random dynamics of free fermions

Understand

We present random quantum circuit models for non-unitary quantum dynamics of free fermions in one spatial dimension.

• Numerical simulations reveal that the dynamics tends towards steady states with logarithmic violations of the entanglement area law and power law correlation functions.
• Moreover, starting with a short-range entangled many-body state, the dynamical evolution of entanglement and correlations quantitatively agrees with the predictions of two-dimensional conformal field theory with a space-like time direction.
• We argue that this behavior is generic in non-unitary free quantum dynamics with time-dependent randomness, and show that the emergent conformal dynamics of two-point functions arises out of a simple "nonlinear master equation".