Abstract
We study the effect of local projective measurements on the quantum quench dynamics. As a concrete example, a one-dimensional Bose-Hubbard model is simulated by the matrix product state and time-evolving block decimation. We map out a global phase diagram in terms of the measurement rate in spatial space and time domain, which demonstrates a volume-to-area law entanglement phase transition. When the measurement rate reaches the critical value, we observe a logarithmic growth of entanglement entropy as the subsystem size or evolved time increases. Moreover, we find that the probability distribution of the single-site entanglement entropy distinguishes the volume and area law phases, similar to the case of disorder-induced many-body localization. We also investigate the scaling behavior of entanglement entropy and mutual information between two separated sites, which is indicative of a single universality class and thus suggests a possible unified description of this transition.
Highlights
Quantum entanglement is an invaluable tool to access the intrinsic nature of underlying states and their nonequilibrium properties in quantum physics [1,2,3]
Our work provides a wealth of evidences that nonunitary factors, such as projective measurements, FIG. 1. (a) A diagrammatic representation of the quench dynamics with local projective measurements
One may naively think that the phase diagram is only controlled by the density of the local projective measurements applied Naver = Nt Px
Summary
Quantum entanglement is an invaluable tool to access the intrinsic nature of underlying states and their nonequilibrium properties in quantum physics [1,2,3]. The presence of the volume-to-area law transition is identified in Floquet and random unitary circuits [36] and can be understood by a classical percolation problem. The scale invariance in critical percolation system exhibits a logarithmic growth of entanglement, and leads to power-law decay correlations. These behaviors are observed in the circuit models by numerics [36,38]. The mutual information is investigated as a measure of quantum correlations between two separated sites and exhibits power-law decay in space Based on these critical entanglement structures, an underlying conformal field theory (CFT) description was proposed. Can induce a dynamical phase transition, adding more pieces of message to the recently proposed theoretical scenario [36,38,39], from the microscopic view on nonintegrable quantum lattice model
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