# Necessary and sufficient conditions for the validity of Luttinger’s theorem

@article{Heath2020NecessaryAS, title={Necessary and sufficient conditions for the validity of Luttinger’s theorem}, author={Joshuah T Heath and Kevin Shawn Bedell}, journal={New Journal of Physics}, year={2020}, volume={22} }

Luttinger’s theorem is a major result in many-body physics that states the volume of the Fermi surface is directly proportional to the particle density. In its ‘hard’ form, Luttinger’s theorem implies that the Fermi volume is invariant with respect to interactions (as opposed to a ‘soft’ Luttinger’s theorem, where this invariance is lost). Despite it is simplicity, the conditions on the fermionic self energy under which Luttinger’s theorem is valid remains a matter of debate, with possible…

## 10 Citations

Luttinger's theorem in the presence of Luttinger surfaces

- PhysicsPhysical Review B
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Breakdown of Landau’s hypothesis of adiabatic continuation from non-interacting to fully interacting electrons is commonly believed to bring about a violation of Luttinger’s theorem. Here, we…

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In periodic systems of interacting electrons, Fermi and Luttinger surfaces refer to the locations within the Brillouin zone of poles and zeros, respectively, of the single-particle Green’s function…

Landau-Fermi liquids in disguise

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- 2021

In periodic systems of interacting electrons, Fermi and Luttinger surfaces refer to the locations within the Brillouin zone of poles and zeros, respectively, of the single-particle Green's function…

Fermi arcs and pseudogap in a lattice model of a doped orthogonal metal

- Physics
- 2021

Since the discovery of the pseudogap and Fermi arc states in underdoped cuprates, the understanding of such non-Fermi-liquid states and the associated violation of Luttinger's theorem have been the…

Landau Quasiparticles in Weak Power-Law Liquids

- Physics
- 2020

The failure of Landau-Fermi liquid theory is often considered a telltale sign of universal, scale-invariant behavior in the emergent field theory of interacting fermions. Nevertheless, there exist…

Universal entanglement signatures of quantum liquids as a guide to fermionic criticality

- Physics
- 2022

An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) in D spatial…

Landau-Fermi liquids without quasiparticles

- Physics
- 2020

Landau-Fermi liquid theory is conventionally believed to hold whenever the interacting single-particle density of states develops a $\delta$-like component at the Fermi surface, which is associated…

Lieb–Schultz–Mattis theorem and the filling constraint

- PhysicsLetters in Mathematical Physics
- 2021

Following recent developments in the classification of bosonic short-range entangled (SRE) phases [1], [2], [3], [4], [5], we examine many-body quantum systems whose ground state fractionalization…

Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System.

- PhysicsPhysical review letters
- 2020

A fundamental concept in physics is the Fermi surface, the constant-energy surface in momentum space encompassing all the occupied quantum states at absolute zero temperature. In 1960, Luttinger…

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