Non-Perturbative Resolution of Luttinger's Theorem Violations in Strongly Correlated Systems
Abstract
Many-body physics faces an apparent paradox concerning violations of Luttinger's theorem in strongly correlated systems. The theorem relates the electron number to the Luttinger count -- the monodromy of the logarithm of the imaginary-frequency Green's function G(iε) -- and, at finite magnetic field, connects the Hall conductivity to the magnetic-field derivative of the Luttinger count via the Streda formula. Here, we provide a non-perturbative solution to this paradox. We demonstrate that the reported violations of Luttinger's theorem do not require a breakdown of the skeleton diagram representation of physical quantities, thereby resolving a long-standing point of contention in many-body theory. Furthermore, we show that the Luttinger integral, which accounts for the mismatch between the particle number and the Luttinger count, is itself a genuine topological invariant directly tied to the Luttinger-Ward functional Φ[G] rather than to the Green's function alone. We demonstrate that this invariant, like the monodromy of ln G(iε) itself, stems exclusively from the zero-frequency discontinuity of the Matsubara trajectory.
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BibTeX
@misc{africani2026nonperturbative,
title = {{Non-Perturbative Resolution of Luttinger's Theorem Violations in Strongly Correlated Systems}},
author = {Nazzareno Africani and Herbert Eßl and Alessandro Toschi and Michele Fabrizio},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07933},
eprint = {2611.07933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07933},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-Perturbative Resolution of Luttinger's Theorem Violations in Strongly Correlated Systems
AU - Nazzareno Africani
AU - Herbert Eßl
AU - Alessandro Toschi
AU - Michele Fabrizio
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07933
UR - https://arxiv.org/abs/2611.07933
AB - Many-body physics faces an apparent paradox concerning violations of Luttinger's theorem in strongly correlated systems. The theorem relates the electron number to the Luttinger count -- the monodromy of the logarithm of the imaginary-frequency Green's function G(iε) -- and, at finite magnetic field, connects the Hall conductivity to the magnetic-field derivative of the Luttinger count via the Streda formula. Here, we provide a non-perturbative solution to this paradox. We demonstrate that the reported violations of Luttinger's theorem do not require a breakdown of the skeleton diagram representation of physical quantities, thereby resolving a long-standing point of contention in many-body theory. Furthermore, we show that the Luttinger integral, which accounts for the mismatch between the particle number and the Luttinger count, is itself a genuine topological invariant directly tied to the Luttinger-Ward functional Φ[G] rather than to the Green's function alone. We demonstrate that this invariant, like the monodromy of ln G(iε) itself, stems exclusively from the zero-frequency discontinuity of the Matsubara trajectory.
ER -