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
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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 | |||||||||
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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 |
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