Eigenstate thermalization in the two-dimensional transverse field Ising model. II. Off-diagonal matrix elements of observables

Rubem Mondaini and Marcos Rigol
Phys. Rev. E 96, 012157 – Published 31 July 2017

Abstract

We study the matrix elements of few-body observables, focusing on the off-diagonal ones, in the eigenstates of the two-dimensional transverse field Ising model. By resolving all symmetries, we relate the onset of quantum chaos to the structure of the matrix elements. In particular, we show that a general result of the theory of random matrices, namely, the value 2 of the ratio of variances (diagonal to off-diagonal) of the matrix elements of Hermitian operators, occurs in the quantum chaotic regime. Furthermore, we explore the behavior of the off-diagonal matrix elements of observables as a function of the eigenstate energy differences and show that it is in accordance with the eigenstate thermalization hypothesis ansatz.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
2 More
  • Received 22 May 2017

DOI:https://doi.org/10.1103/PhysRevE.96.012157

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Rubem Mondaini1 and Marcos Rigol2

  • 1Beijing Computational Science Research Center, Beijing 100193, China
  • 2Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA

See Also

Eigenstate thermalization in the two-dimensional transverse field Ising model

Rubem Mondaini, Keith R. Fratus, Mark Srednicki, and Marcos Rigol
Phys. Rev. E 93, 032104 (2016)

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 96, Iss. 1 — July 2017

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
×