Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems (B2)

Maximilian Kiefer-Emmanouilidis, Razmik Unanyan, Jesko Sirker, and Michael Fleischhauer:

🔓 SciPost Physics, 8, 083 (2020)

Entanglement in a pure state of a many-body system can be characterized by the R\'enyi entropies S^(α)=lntr(ρ^α)/(1−α) of the reduced density matrix ρ of a subsystem. These entropies are, however, difficult to access experimentally and can typically be determined for small systems only. Here we show that for free fermionic systems in a Gaussian state and with particle number conservation, ln S⁽²⁾ can be tightly bound---from above and below---by the much easier accessible R\'enyi number entropy S_N⁽²⁾=−ln∑_np²(n) which is a function of the probability distribution p(n) of the total particle number in the considered subsystem only. A dynamical growth in entanglement, in particular, is therefore always accompanied by a growth---albeit logarithmically slower---of the number entropy. We illustrate this relation by presenting numerical results for quenches in non-interacting one-dimensional lattice models including disorder-free, Anderson-localized, and critical systems with off-diagonal disorder.