Abstract
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".
Highlights
Recent years have seen a surge of interest in manybody quantum dynamics generated by random unitary circuits [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]
At late times, we recover Eq (14). Based on these numerical results, we conjecture that this nonunitary dynamics has emergent two-dimensional conformal symmetry: namely, the state is obtained through conformal field theory (CFT) Hamilontian under purely imaginary time evolution, as in Eq (1)
We construct a one-dimensional nonunitary free fermion circuit model with nontrivial steady state. We demonstrate that this model has emergent criticality and has two-dimensional conformal symmetry
Summary
Recent years have seen a surge of interest in manybody quantum dynamics generated by random unitary circuits [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. Note that to observe this transition, we need to follow the quantum trajectory of the many-body wave function rather than the evolution of the density matrix described by the Kraus map [37] or its Markovian version, the Lindblad equation [38] Motivated by these studies, in this paper we introduce a model of random nonunitary dynamics for free fermions. Model consists of discrete time evolution, with alternating application of unitary gates (nearest-neighbor hopping gates), nonunitary gates (evolving with on-site potential in imaginary time), and wave function renormalization This model is different than a free fermion model subjected to projective measurement [20,23], in which any nonzero measurement rate drives the system to a trivial quantum Zeno phase with area law entanglement. VI, we summarize our results and discuss several interesting directions for future work
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