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Published October 2002 | metadata_only
Journal Article

On the Distribution of Eigenvalues of Grand Canonical Density Matrices


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.

Additional Information

© 2002 Plenum Publishing Corporation. Received April 2, 2002; accepted May 2, 2002.

Additional details

August 21, 2023
August 21, 2023