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in the case of noninteracting particles, it remains true even as interactions between particles are taken into consideration provided that the appropriate definitions of Fermi surface and particle density are adopted. Specifically, in the interacting case the Fermi surface must be defined according
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Behnam Farid (2009). "Comment on "Violation of the
Luttinger sum rule within the Hubbard model on a triangular lattice", by J. Kokalj and P. Prelovšek,
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Behnam Farid; Tsvelik (2009). "Comment on "Breakdown of the
Luttinger sum rule within the Mott-Hubbard insulator", by J. Kokalj and P. Prelovšek,
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Behnam Farid (2007). "On the
Luttinger theorem concerning number of particles in the ground states of systems of interacting fermions".
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Proceedings of the
International School of Physics "Enrico Fermi", Course CXXI "Perspectives in Many-Particle Physics"
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Luttinger, J. M. (1960). "Fermi
Surface and Some Simple Equilibrium Properties of a System of Interacting Fermions".
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M. Oshikawa (2000). "Topological
Approach to Luttinger's Theorem and the Fermi Surface of a Kondo Lattice".
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F. D. M. Haldane (2005). "Luttinger's
Theorem and Bosonization of the Fermi Surface". In R. A. Broglia;
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the volume enclosed by a material's Fermi surface is directly proportional to the particle density
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Luttinger's theorem relates a Fermi liquid's particle density to the volume of its Fermi surface.
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Kiaran B. Dave; Philip W. Phillips; Charles L. Kane (2013). "Absence of
Luttinger's theorem".
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295:{\displaystyle n=2\int _{{\mathcal {Re\,}}G(\omega =0,k)>0}{\frac {d^{D}k}{(2\pi )^{D}}}}
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transport. It arises frequently in theoretical models of correlated electrons, such as the
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Luttinger, J. M.; Ward, J. C. (1960). "Ground-State Energy of a Many-Fermion System. II".
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Luttinger Model: The First 50 Years and Some New
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in 1960 that has broad implications in the field of
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143:{\displaystyle \infty ,}
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437:References
391:-space in
60:Definition
38:J. C. Ward
630:1207.4201
607:0909.2887
588:0909.2886
569:0711.0952
539:cite book
277:π
227:ω
206:∫
179:frequency
135:∞
112:→
93:ω
48:, and in
817:Fermions
766:(eds.).
712:11019092
655:23496693
415:See also
183:momentum
42:electron
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720:9806160
692:Bibcode
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635:Bibcode
556:General
504:Bibcode
467:Bibcode
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442:Inline
306:where
153:where
776:arXiv
716:S2CID
682:arXiv
659:S2CID
625:arXiv
602:arXiv
583:arXiv
564:arXiv
127:or
749:ISBN
708:PMID
651:PMID
545:link
341:and
245:>
181:and
36:and
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