Quantum criticality in the nonunitary dynamics of (2+1)-dimensional free fermions

We explore the nonunitary dynamics of (2 + 1)-dimensional free fermions and show that the obtained steady state is critical regardless the strength of the nonunitary evolution. Numerical results indicate that the entanglement entropy has a logarithmic violation of the area law and the mutual information between two distant regions decays as a power-law function. In particular, we provide an interpretation of these scaling behaviors in terms of a simple quasiparticle pair picture. In addition, we study the dynamics of the correlation function and demonstrate that this system has dynamical exponent z = 1. We further demonstrate the dynamics of the correlation function can be well captured by a classical nonlinear master equation. Our method opens a door to a vast number of nonunitary random dynamics in free fermions and can be generalized to any dimensions.

Automated summary

The nonunitary dynamics of (2 + 1)-dimensional free fermions result in a critical steady state regardless of the strength of the nonunitary evolution. Numerical results show a logarithmic violation of the area law for entanglement entropy and decay of mutual information between distant regions as a power-law function. Additionally, the study demonstrates a dynamical exponent of z = 1 and the ability to capture the dynamics of the correlation function with a classical nonlinear master equation.