## Absence of Luttinger's theorem for fermions with power-law Green functions

Kridsanaphong Limtragool, Zhidong Leong, Philip W. Phillips

SciPost Phys. 5, 049 (2018) · published 16 November 2018

- doi: 10.21468/SciPostPhys.5.5.049
- Submissions/Reports

### Abstract

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 with power-law Green functions which do not necessarily preserve particle-hole symmetry. However, Ref. \cite{Blagoev1997,Yamanaka1997} showed that Luttinger liquids, another scale-invariant fermionic model, respect Luttinger's theorem. To understand the difference, we examine the spinless Luttinger liquid model. We find two properties which make the Luttinger sum rule valid in this model: particle-hole symmetry and $\mathrm{Im} G(\omega=0,-\infty)=0$. We conjecture that these two properties represent sufficient, but not necessary, conditions for the validity of the Luttinger sum rule in condensed matter systems.

### Cited by 4

### Authors / Affiliation: mappings to Contributors and Organizations

See all Organizations.-
^{1}Kridsanaphong Limtragool, -
^{1}Zhidong Leong, -
^{1}Philip Phillips

- Ministry of Science and Technology of Thailand (through Organization: กระทรวงวิทยาศาสตร์และเทคโนโลยี / Ministry of Science and Technology Thailand [MOST])
- National Science Foundation [NSF]
- University of Illinois at Urbana-Champaign (through Organization: University of Illinois at Urbana Champaign [UIUC])