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arXiv:2101.04320 · Physical review. B./Physical review. B

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

Qicheng Tang, Xiao Dong Chen, W. Zhu

Published May 12, 2021• 65 citations
arXivHTMLPDF

Abstract

Quantum criticality, which exhibits universal features such as nontrivial collective fluctuations, is one of the central topics in statistical and condensed matter physics. Here, the authors design a class of nonunitary random dynamics of free fermions that robustly produces novel critical steady states. The emergent quantum criticality is numerically confirmed for the 2+1 dimensional case, and the proposed analytical interpretation can be easily extended to any dimensions. Their discoveries are potentially helpful to understand quantum critical phenomenon in nonequilibrium dynamics.

DOI
10.1103/physrevb.103.174303

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We explore, both analytically and numerically, the quantum dynamics of a many-body free-fermion system subjected to local density measurements. We begin by extending the mapping to the nonlinear sigma-model (NLSM) field theory for the case of finite evolution time T and different classes of initial states, which lead to different NLSM boundary conditions. The analytical formalism is then used to study how quantum correlations gradually develop, with increasing T , from those determined by the initial state towards their steady-state form. The analytical results are confirmed by numerical simulations for several types of initial states. We further consider the long-time limit, when the system in d + 1 space-time dimensions becomes quasi-one-dimensional, and analyze the scaling of the “localization” time (which is simultaneously the purification time and the charge-sharpening time for this class of problems). The analytical predictions for scaling properties are fully confirmed by numerical simulations in a d = 2 model around the measurement-induced phase transition. We use this dynamical approach to determine numerically the measurement-induced transition point and the associated correlation-length critical exponent.
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