Typical entanglement entropy in systems with particle-number conservation

TL;DR

This paper derives a universal formula for the typical bipartite entanglement entropy in particle-number conserving systems, applicable to various particle types and system models, highlighting differences between chaotic and integrable systems.

Contribution

It provides a universal power series expansion for entanglement entropy in systems with particle-number conservation, applicable across different particle types and system models.

Findings

Universal entanglement entropy formula derived

Entropy behavior differs between chaotic and integrable systems

Results validated across bosons, fermions, spins, and mixtures

Abstract

We calculate the typical bipartite entanglement entropy $\langle S_A\rangle_N$ in systems containing indistinguishable particles of any kind as a function of the total particle number $N$, the volume $V$, and the subsystem fraction $f=V_A/V$, where $V_A$ is the volume of the subsystem. We expand our result as a power series $\langle S_A\rangle_N=a f V+b\sqrt{V}+c+o(1)$, and find that $c$ is universal (i.e., independent of the system type), while $a$ and $b$ can be obtained from a generating function characterizing the local Hilbert space dimension. We illustrate the generality of our findings by studying a wide range of different systems, e.g., bosons, fermions, spins, and mixtures thereof. We provide evidence that our analytical results describe the entanglement entropy of highly excited eigenstates of quantum-chaotic spin and boson systems, which is distinct from that of integrable counterparts.