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

Abstract

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.

6 pages and 6 figures (main text) + 19 pages and 18 figures (appendices)

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• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Topological transitions with continuously monitored free fermions
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• Density and current statistics in boundary-driven monitored fermionic chains
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• Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
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• Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain