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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.

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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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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
Record Number:CaltechAUTHORS:20161220-095020187
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72970
Deposited By: Donna Wrublewski
Deposited On:20 Dec 2016 18:53
Last Modified:11 Nov 2021 05:09

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