• Editors' Suggestion

Bipartite fluctuations as a probe of many-body entanglement

H. Francis Song, Stephan Rachel, Christian Flindt, Israel Klich, Nicolas Laflorencie, and Karyn Le Hur
Phys. Rev. B 85, 035409 – Published 6 January 2012
PDFHTMLExport Citation

Abstract

We investigate in detail the behavior of the bipartite fluctuations of particle number N̂ and spin Ŝz 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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
10 More
  • Received 6 October 2011

DOI:https://doi.org/10.1103/PhysRevB.85.035409

©2012 American Physical Society

Authors & Affiliations

H. Francis Song1, Stephan Rachel1, Christian Flindt2, Israel Klich3, Nicolas Laflorencie4, and Karyn Le Hur1

  • 1Department of Physics, Yale University, New Haven, Connecticut 06520, USA
  • 2Département de Physique Théorique, Université de Genève, CH-1211 Genève, Switzerland
  • 3Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
  • 4Laboratoire de Physique Théorique, Université de Toulouse, UPS, (IRSAMC), Toulouse, France

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 85, Iss. 3 — 15 January 2012

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×