Luttinger theorem and low energy properties of ideal Haldane-Sutherland Liquids

TL;DR

This paper explores how Haldane-Sutherland liquids, which obey exclusion statistics due to interaction-induced displacement fields, still conform to Luttinger's theorem, resulting in Fermi-liquid-like low energy behavior.

Contribution

It demonstrates the compatibility of Luttinger's theorem with exclusion statistics in Haldane-Sutherland liquids through momentum conservation and adiabaticity.

Findings

Luttinger's theorem remains valid in Haldane-Sutherland liquids.

Low energy properties are similar to Fermi or Luttinger liquids.

Exclusion statistics originate from interaction-induced displacement fields.

Abstract

We study in this paper the properties of a many body system of fermions obeying exclusion-statistics (Haldane liquid) where the origin of exclusion statistics is coming from an interaction-induced displacement field $\mathbf{a}_{\mathbf{k}}$ introduced by Sutherland (Haldane-Sutherland liquid). In particular we show how the Luttinger Theorem becomes compatible with exclusion statistics as a result of momentum conservation and adiabaticity. As a result, the low energy properties of Haldane-Sutherland liquids are Fermi/Luttinger liquid-like.