Non-perturbative conserving approximations and Luttinger's sum rule |
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Authors: | J Ortloff M Balzer M Potthoff |
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Institution: | 1. Institut für Theoretische Physik und Astrophysik, Universit?t Würzburg, Am Hubland, 97074, Würzburg, Germany
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Abstract: | Weak-coupling conserving approximations can be constructed by truncations of the
Luttinger-Ward functional and are well known as thermodynamically consistent approaches
which respect macroscopic conservation laws as well as certain sum rules at zero temperature.
These properties can also be shown for variational approximations that are generated
within the framework of the self-energy-functional theory without a truncation of the
diagram series.
Luttinger's sum rule represents an exception.
We analyze the conditions under which the sum rule holds within a non-perturbative
conserving approximation.
Numerical examples are given for a simple but non-trivial dynamical two-site approximation.
The validity of the sum rule for finite Hubbard clusters and the consequences for cluster
extensions of the dynamical mean-field theory are discussed. |
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Keywords: | 71 10 -w Theories and models of many-electron systems 71 10 Fd Lattice fermion models |
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