Boson-fermion universality of mesoscopic entanglement fluctuations in free systems

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>∼</a:mo><a:mn>1</a:mn><a:mo>/</a:mo><a:mi>L</a:mi></a:mrow></a:math> to <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mo>∼</b:mo><b:msubsup><b:mi>L</b:mi><b:mi>A</b:mi><b:mn>3</b:mn></b:msubsup><b:mo>/</b:mo><b:msup><b:mi>L</b:mi><b:mn>2</b:mn></b:msup></b:mrow></b:math> as the subsystem size <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>L</c:mi><c:mi>A</c:mi></c:msub></c:math> increases (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>L</d:mi></d:math> 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.