Bipartite fluctuations as a probe of many-body entanglement

H. Francis Song*, Stephan Rachel, Christian Flindt, Israel Klich, Nicolas Laflorencie, Karyn Le Hur

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

159 Citations (Scopus)


We investigate in detail the behavior of the bipartite fluctuations of particle number N and spin Sz in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and full counting statistics have been used in mesoscopic transport and cold-atomic gases. For systems that can be mapped to a problem of noninteracting fermions, we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection, we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization-group and quantum Monte Carlo calculations, and in principle accessible in condensed-matter and cold-atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

Original languageEnglish
Article number035409
Pages (from-to)1-27
Number of pages27
JournalPhysical Review B
Issue number3
Publication statusPublished - 6 Jan 2012
MoE publication typeA1 Journal article-refereed

Fingerprint Dive into the research topics of 'Bipartite fluctuations as a probe of many-body entanglement'. Together they form a unique fingerprint.

Cite this