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Boson-fermion universality of mesoscopic entanglement fluctuations in free systems

Cunzhong Lou1,2,*, Chushun Tian2,*, Zhixing Zou3,2, Tao Shi2, and Lih-King Lim1,†

  • *These authors contributed equally to this work.
  • †Contact author: lihking@zju.edu.cn
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Phys. Rev. Research 7, 023297 – Published 24 June, 2025

DOI: https://doi.org/10.1103/jhlh-pcm9

Abstract

Entanglement fluctuations associated with the Schrödinger evolution of wave functions offer a unique perspective on various fundamental issues ranging from quantum thermalization to state preparation in quantum devices. Very recently, a subset of the present authors showed that, in a class of free-fermion lattice models and interacting spin chains, entanglement dynamics enters into a new regime at long time, with entanglement probes displaying persistent temporal fluctuations, whose statistics falls into the seemingly disparate paradigm of mesoscopic fluctuations in condensed-matter physics. This motivates us to revisit here entanglement dynamics of a canonical bosonic model in many-body physics, i.e., a coupled harmonic oscillator chain. We find that when the system is driven out of equilibrium, the long-time entanglement dynamics exhibits strictly the same statistical behaviors as those of free-fermion models. Specifically, irrespective of entanglement probes and microscopic parameters, the statistical distribution of entanglement fluctuations is flanked by asymmetric tails: sub-Gaussian for upward fluctuations and sub-Gamma for downward; moreover, the variance exhibits a crossover from the scaling ∼1/L to ∼LA3/L2 as the subsystem size LA increases (L the total system size). This insensitivity to the particle statistics, dubbed boson-fermion universality, is contrary to the common wisdom that statistical phenomena of a many-body nature depend strongly on particle statistics. Together with our previous work, the present study indicates rich fluctuation phenomena in long-time entanglement dynamics that await in-depth exploration.

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Phys. Rev. Research 7, 023297– Published 24 June, 2025
  • Received 18 November 2024
  • Accepted 30 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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