• Rapid Communication

Weak and strong typicality in quantum systems

Lea F. Santos, Anatoli Polkovnikov, and Marcos Rigol
Phys. Rev. E 86, 010102(R) – Published 5 July 2012
PDFHTMLExport Citation

Abstract

We study the properties of mixed states obtained from eigenstates of many-body lattice Hamiltonians after tracing out part of the lattice. Two scenarios emerge for generic systems: (i) The diagonal entropy becomes equivalent to the thermodynamic entropy when a few sites are traced out (weak typicality); and (ii) the von Neumann (entanglement) entropy becomes equivalent to the thermodynamic entropy when a large fraction of the lattice is traced out (strong typicality). Remarkably, the results for few-body observables obtained with the reduced, diagonal, and canonical density matrices are very similar to each other, no matter which fraction of the lattice is traced out. Hence, for all physical quantities studied here, the results in the diagonal ensemble match the thermal predictions.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 21 February 2012

DOI:https://doi.org/10.1103/PhysRevE.86.010102

©2012 American Physical Society

Authors & Affiliations

Lea F. Santos1, Anatoli Polkovnikov2, and Marcos Rigol3,4

  • 1Department of Physics, Yeshiva University, New York, New York 10016, USA
  • 2Department of Physics, Boston University, Boston, Massachusetts 02215, USA
  • 3Department of Physics, Georgetown University, Washington, DC 20057, USA
  • 4Physics Department, The Pennsylvania State University, 104 Davey Laboratory, University Park, Pennsylvania 16802, USA

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 86, Iss. 1 — July 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 E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×