Journal
NEW JOURNAL OF PHYSICS
Volume 22, Issue 6, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/ab890e
Keywords
Luttinger's theorem; anomalies; index theorem; self-energy; Kadanoff-Baym; Landau-Fermi liquids; cuprates
Categories
Funding
- John H Rourke endowment fund at Boston College
Ask authors/readers for more resources
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 requirements for its validity ranging from particle-hole symmetry to analyticity about the Fermi surface. In this paper, we propose the minimal requirements for the application of a hard Luttinger's theorem to a generic fermionic system of arbitrary interaction strength by invoking the Atiyah-Singer index theorem to quantify the topologically-robust behavior of a generalized Fermi surface. We show that the applicability of a hard Luttinger's theorem in aD-dimensional system is directly dependent on the existence of a (D- 1)-dimensional manifold of gapless chiral excitations at the Fermi level, regardless of whether the system exhibits Luttinger or Fermi surfaces (i.e., manifolds of zeroes of the Green's function and inverse Green's function, respectively). The exact form of the self-energy which guarantees validity of a hard Luttinger's theorem is derived, and agreement with current experiments, numerics, and theories are discussed.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available