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arXiv:2005.13603 · Physical Review Research

Measurement-induced entanglement transitions in many-body localized systems

Oliver Lunt, Arijeet Pal

Published Oct 14, 2020• 132 citations
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Abstract

The authors show that many-body localized systems can have a volume-law which is stable against measurements, but only for certain measurement bases, and explain it on the basis of an an interplay between the measurements and the system's integrals of motion.
DOI
10.1103/physrevresearch.2.043072

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Quantum information tends to spread out in interacting systems, leading to thermalization as characterized by the volume-law entropy of entanglement, while local measurements that extract classical information of the state tend to interrupt the propagation of information and reduce the entanglement entropy. Can entanglement sustain repeated measurements? The authors address this question in a toy hybrid-circuit model, where qubits undergo both unitary time evolution and sporadic local measurements. The phase diagram features a stable volume-law phase of entanglement for weak measurements and an area-law phase for strong measurements. The two domains in the diagram are separated by a single second-order phase transition. Characterization of both phases as well as of the critical point are presented.
We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion, which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggest a direct transition between the two phases.