Typical entanglement entropy in systems with particle-number conservation

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.