Non-perturbative conserving approximations and Luttinger's sum rule

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.

13 pages, 10 figures, revised version with slightly extended discussion, accepted by EPJB

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Cited by in corpus (14)

• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Topological interpretation of Luttinger theorem
• Mott transition in one dimension: Benchmarking dynamical cluster approaches
• Self-energy and Fermi surface of the 2-dimensional Hubbard model
• Variational cluster approach for strongly correlated lattice bosons in the superfluid phase
• Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band Hubbard model at half filling
• Variational cluster approach to ferromagnetism in infinite dimensions and in one-dimensional chains
• Partial self-consistency and analyticity in many-body perturbation theory: particle number conservation and a generalized sum rule
• Variational cluster approach to superconductivity and magnetism in the Kondo lattice model
• Breakdown of the Luttinger sum rule within the Mott-Hubbard insulator
• Luttinger theorem and imbalanced Fermi systems
• Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice
• Violation of Luttinger's theorem in the simplest doped Mott insulator: Falicov-Kimball model in strong correlation limit
• Thermodynamic properties of two-component fermionic atoms trapped in a two-dimensional optical lattice