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… 
Luttinger's theorem in the presence of Luttinger surfaces
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
Emergent quasiparticles at Luttinger surfaces
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
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
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
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
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
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
  • Hank Chen
  • Physics
    Letters 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.
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

References

SHOWING 1-10 OF 227 REFERENCES
Absence of Luttinger's theorem for fermions with power-law Green functions
We investigate the validity of Luttinger’s theorem (or Luttinger sum rule) in two scale-invariant fermionic models. We find that, in general, Luttinger’s theorem does not hold in a system of fermions
Topological interpretation of the Luttinger theorem
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological
A Luttinger's theorem revisited
Abstract For uniform systems of spinless fermions in d spatial dimensions with d > 1, interacting through the isotropic two-body potential ν(r -r′), a celebrated theorem due to Luttinger (1961)
Absence of Luttinger's theorem due to zeros in the single-particle Green function.
We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, μ, for a T=0 gapped system is removed by using the unique value
Luttinger theorem and imbalanced Fermi systems
Abstract The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is
Much Ado about Zeros: The Luttinger Surface and Mottness
We prove that the Mott insulating state is characterized by a divergence of the electron self energy at well-defined values of momenta in the first Brillouin zone. When particle-hole symmetry is
Exact Solution of a Many-Fermion System and Its Associated Boson Field
Luttinger’s exactly soluble model of a one-dimensional many-fermion system is discussed. We show that he did not solve his model properly because of the paradoxical fact that the density operator
NONPERTURBATIVE APPROACH TO LUTTINGER'S THEOREM IN ONE DIMENSION
The Lieb-Schultz-Mattis theorem for spin chains is generalized to a wide range of models of interacting electrons and localized spins on a one dimensional lattice. The existence of a low-energy state
Non-Perturbative Many-Body Approach to the Hubbard Model and Single-Particle Pseudogap
A new approach to the single-band Hubbard model is described in the general context of many-body theories. It is based on enforcing conservation laws, the Pauli principle and a number of crucial
Some consequences of the Luttinger theorem: The Luttinger surfaces in non-Fermi liquids and Mott insulators
Landau and Luttinger have shown that the properties of so-called Fermi liquids are determined by the Fermi surface of their excitations. The present analysis of mathematics of the Luttinger paper
...
...