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

References in corpus (6)

• Variational cluster approach to correlated electron systems in low dimensions
• Variational cluster approach to spontaneous symmetry breaking: The itinerant antiferromagnet in two dimensions
• Self-energy-functional approach: Analytical results and the Mott-Hubbard transition
• First- and Second Order Phase Transitions in the Holstein-Hubbard Model
• Phase separation in the particle-hole asymmetric Hubbard model
• Luttinger sum rule for finite systems of correlated electrons

Cited by in corpus (4)

• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Mott transition in one dimension: Benchmarking dynamical cluster approaches
• Breakdown of the Luttinger sum rule within the Mott-Hubbard insulator
• Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice