Boson-fermion universality of mesoscopic entanglement fluctuations in free systems

TL;DR

This paper reveals a universal statistical behavior of long-time entanglement fluctuations in free bosonic and fermionic systems, showing insensitivity to particle statistics and uncovering new fluctuation regimes in many-body quantum dynamics.

Contribution

It demonstrates boson-fermion universality in entanglement fluctuations during non-equilibrium dynamics of free systems, extending previous fermionic results to bosonic models.

Findings

Entanglement fluctuations follow asymmetric sub-Gaussian and sub-Gamma distributions.

Variance scales crossover from 1/L to L_A^3/L^2 with subsystem size.

Universal behavior independent of particle statistics observed in long-time entanglement dynamics.

Abstract

Entanglement fluctuations associated with Schr\"{o}dinger evolution of wavefunctions offer a unique perspective on various fundamental issues ranging from quantum thermalization to state preparation in quantum devices. Very recently, a subset of present authors have shown 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 motivate 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 that 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 $\sim 1/L$ to $\sim L_A^3/L^2$, 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 many-body nature depend strongly on particle statistics. Together with our previous work, the present work indicates rich fluctuation phenomena in entanglement dynamics awaiting in-depth explorations.