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arXiv:2301.07290 · Physical review. B./Physical review. B

Localization properties in disordered quantum many-body dynamics under continuous measurement

Kazuki Yamamoto, Ryusuke Hamazaki

Published Jun 7, 2023• 37 citations
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Abstract

We study the localization properties of continuously monitored dynamics and associated measurement-induced phase transitions in disordered quantum many-body systems on the basis of the quantum trajectory approach. By calculating the fidelity between random quantum trajectories, we demonstrate that the disorder and the measurement can lead to dynamical properties distinct from each other, although both have a power to suppress the entanglement spreading. In particular, in the large-disorder regime with weak measurement, we elucidate that the fidelity exhibits an anomalous power-law decay before saturating to the steady-state value. Furthermore, we propose a general method to access physical quantities for quantum trajectories in continuously monitored dynamics without postselection. It is demonstrated that this scheme drastically reduces the cost of experiments. Our results can be tested in ultracold atoms subject to continuous measurement and open the avenue to study the dynamical properties of localization, which cannot be understood from the stationary properties of the entanglement entropy.

DOI
10.1103/physrevb.107.l220201

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We study the localization properties of continuously monitored dynamics and associated measurement-induced phase transitions in disordered quantum many-body systems on the basis of the quantum trajectory approach. By calculating the fidelity between random quantum trajectories, we demonstrate that the disorder and the measurement can lead to dynamical properties distinct from each other, although both have a power to suppress the entanglement spreading. In particular, in the large-disorder regime with weak measurement, we elucidate that the fidelity exhibits an anomalous power-law decay before saturating to the steady-state value. Furthermore, we propose a general method to access physical quantities for quantum trajectories in continuously monitored dynamics without postselection. It is demonstrated that this scheme drastically reduces the cost of experiments. Our results can be tested in ultracold atoms subject to continuous measurement and open the avenue to study the dynamical properties of localization, which cannot be understood from the stationary properties of the entanglement entropy.
Localization, which is typically induced by disorder, is an exotic phenomenon where a quantum state fails to spread over the entire Hilbert space. Recently, measurement is utilized as another mechanism to localize a quantum state in nonunitary quantum circuits and continuously monitored systems, which exhibit novel quantum phenomena dubbed measurement-induced phase transitions (MIPTs). However, while both the disorder and the measurement localize the wave function and suppress the entanglement spreading, it is still not clear whether they exhibit the same localization properties. In this seminar, we study localization properties of continuously monitored dynamics and associated MIPTs in disordered quantum many-body systems on the basis of the quantum trajectory approach [1]. By calculating the fidelity between random quantum trajectories, we demonstrate that the disorder and the measurement can lead to dynamical properties distinct from each other, although both have a power to suppress the entanglement spreading. In particular, in the large-disorder regime with weak measurement, we elucidate that the fidelity exhibits an anomalous power-law decay before saturating to the steady-state value. Furthermore, we propose a general method to access physical quantities for quantum trajectories in continuously monitored dynamics without resorting to postselection. It is argued that this scheme drastically reduces the cost of experiments. Our results can be tested in ultracold atoms subject to continuous measurement. Reference [1] K. Yamamoto and R. Hamazaki, arXiv:2301.07291, Phys. Rev. B (Letter) in press.
We investigate entanglement phase transitions from volume-law to area-law entanglement in a quantum many-body state under continuous position measurement on the basis of the quantum trajectory approach. We find the signatures of the transitions as peak structures in the mutual information as a function of measurement strength, as previously reported for random unitary circuits with projective measurements. At the transition points, the entanglement entropy scales logarithmically and various physical quantities scale algebraically, implying emergent conformal criticality, for both integrable and nonintegrable one-dimensional interacting Hamiltonians; however, such transitions have been argued to be absent in noninteracting regimes in some previous studies. With the aid of U(1)U(1)U(1) symmetry in our model, the measurement-induced criticality exhibits a spectral signature resembling a Tomonaga-Luttinger liquid theory from symmetry-resolved entanglement. These intriguing critical phenomena are unique to steady-state regimes of the conditional dynamics at the single-trajectory level and are absent in the unconditional dynamics obeying the Lindblad master equation, in which the system ends up with the featureless, infinite-temperature mixed state. We also propose a possible experimental setup to test the predicted entanglement transition based on the subsystem particle-number fluctuations. This quantity should readily be measured by the current techniques of quantum gas microscopy and is in practice easier to obtain than the entanglement entropy itself.
Wavefunction collapse is commonly associated with unavoidable physical disturbance of the measured system. Here we show that in driven-dissipative quantum systems, continuous measurement can induce strong trajectory-level collapse while leaving the ensemble-averaged steady state strictly invariant. We identify measurement-invariant steady states whose unconditional density matrix remains unchanged under continuous monitoring, despite pronounced measurement-induced localization in conditioned quantum trajectories. This separation between trajectory-level collapse and ensemble invariance defines a regime of partial collapse, in which measurement-induced localization is continuously counteracted by dissipative dynamics. We derive a necessary and sufficient condition for steady-state invariance under continuous measurement and identify Liouvillian symmetry as a concrete dynamical mechanism enforcing it. Our results clarify the distinction between conditional collapse and physical disturbance in open quantum systems and provide a framework for non-invasive continuous monitoring in driven-dissipative settings.
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We investigate measurement-induced localization in a continuously monitored one-dimensional Aubry--André--Harper model, focusing on the quantum Zeno regime in which the measurements dominate coherent dynamics. The presence of a quasiperiodic potential renders the problem analytically tractable and enables a controlled study of the interplay between monitoring and disorder. We develop an analytical description based on an instantaneous Schrödinger equation with a measurement-induced effective potential constructed self-consistently from individual quantum trajectories, without relying on postselection. In the quantum Zeno regime, an emergent dominant energy scale reduces the problem to a transfer-matrix formulation of an effective non-Hermitian Hamiltonian, which allows direct computation of the Lyapunov exponent. Complementarily, we extract the localization length numerically from long-time steady-state quantum state diffusion trajectories by reconstructing the intrinsic localized single-particle wave functions and analyzing their spatial decay. These numerical results show quantitative agreement with the effective theory predictions, with controlled corrections of order J2/[λ2+(γ/2)2]J^2/[λ^2+(γ/2)^2]J2/[λ2+(γ/2)2] (where JJJ is the hopping amplitude, γγγ the measurement strength, and λλλ the quasiperiodic potential). Our results underscore the connection between the effective non-Hermitian description and the stochastic monitored dynamics, showing the interplay between Zeno-like localization, coherent hopping, and quasiperiodic-disorder-induced localization, while also laying the groundwork for understanding and exploiting measurement-induced localization as a tool for quantum control and state preparation.
We study the properties of a monitored ensemble of atoms driven by a laser field and in the presence of collective decay. The properties of the quantum trajectories describing the atomic cloud drastically depend on the monitoring protocol and are distinct from those of the average density matrix. By varying the strength of the external drive, a measurement-induced phase transition occurs separating two phases with entanglement entropy scaling subextensively with the system size. Incidentally, the critical point coincides with the superradiance transition of the trajectory-averaged dynamics. Our setup is implementable in current light-matter interaction devices, and most notably, the monitored dynamics is free from the postselection measurement problem, even in the case of imperfect monitoring.