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

Kiefer-Emmanouilidis M, Unanyan R, Sirker J, Fleischhauer M (2020)

Publication Type: Journal article

Publication year: 2020

Journal

SciPost Physics SciPost

Book Volume: 8

Article Number: 083

Journal Issue: 6

DOI: 10.21468/SciPostPhys.8.6.083

Abstract

Entanglement in a pure state of a many-body system can be characterized by the Rényi entropies S(α) = ln tr(ρα)/(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, S(2) can be tightly bound—from above and below—by the much easier accessible Rényi number entropy S(N2) = − ln Pn p2(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 noninteracting one-dimensional lattice models including disorder-free, Anderson-localized, and critical systems with off-diagonal (bond) disorder.

Involved external institutions

Technische Universität Kaiserslautern DE Germany (DE) University of Manitoba CA Canada (CA)

How to cite

APA:

Kiefer-Emmanouilidis, M., Unanyan, R., Sirker, J., & Fleischhauer, M. (2020). Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems. SciPost Physics, 8(6). https://dx.doi.org/10.21468/SciPostPhys.8.6.083

MLA:

Kiefer-Emmanouilidis, Maximilian, et al. "Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems." SciPost Physics 8.6 (2020).

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