CaltechAUTHORS
  A Caltech Library Service

On the Distribution of Eigenvalues of Grand Canonical Density Matrices

Chan, Garnet Kin-Lic and Ayers, Paul W. and Croot, Ernest S., III (2002) On the Distribution of Eigenvalues of Grand Canonical Density Matrices. Journal of Statistical Physics, 109 (1/2). pp. 289-299. ISSN 0022-4715. doi:10.1023/A:1019999930923. https://resolver.caltech.edu/CaltechAUTHORS:20161220-095020187

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20161220-095020187

Abstract

Using physical arguments and partition theoretic methods, we demonstrate under general conditions, that the eigenvalues w(m) of the grand canonical density matrix decay rapidly with their index m, like w(m)∼exp[−βB−1(ln m)1+1/α], where B and α are positive constants, O(1), which may be computed from the spectrum of the Hamiltonian. We compute values of B and α for several physical models, and confirm our theoretical predictions with numerical experiments. Our results have implications in a variety of questions, including the behaviour of fluctuations in ensembles, and the convergence of numerical density matrix renormalization group techniques.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org10.1023/A:1019999930923DOIArticle
http://link.springer.com/article/10.1023/A:1019999930923PublisherArticle
ORCID:
AuthorORCID
Chan, Garnet Kin-Lic0000-0001-8009-6038
Additional Information:© 2002 Plenum Publishing Corporation. Received April 2, 2002; accepted May 2, 2002.
Subject Keywords:Grand canonical ensemble; density matrix eigenvalues; partition theory; renormalization group; fluctuations
Issue or Number:1/2
DOI:10.1023/A:1019999930923
Record Number:CaltechAUTHORS:20161220-095020187
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161220-095020187
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72970
Collection:CaltechAUTHORS
Deposited By: Donna Wrublewski
Deposited On:20 Dec 2016 18:53
Last Modified:11 Nov 2021 05:09

Repository Staff Only: item control page