Boson-fermion universality of mesoscopic entanglement fluctuations in free systems - Cunzhong Lou; Chushun Tian; Zhixing Zou; Tao Shi; Lih-King Lim (Physical Review Research)
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 ∼L_{A}^{3}/L^{2} as the subsystem size L_{A} 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.