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arXiv:1801.02848

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

Tai Kai Ng

Published Jan 9, 2018• 0 citations
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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.

DOI
10.48550/arxiv.1801.02848

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We propose in this paper an effective low-energy theory for interacting fermion systems which supports exclusion statistics. The theory can be viewed as an extension of Landau Fermi liquid theory where besides quasi-particle energy ξkξ_{\mathbf{k}}ξk​, the kinetic momentum k\mathbf{k}k of quasi-particles depends also on quasi-particle occupation numbers as a result of momentum (kkk)-dependent current-current interaction. The dependence of kinetic momentum on quasi-particles excitations leads to change in density of states and exclusion statistics. The properties of this new Fermi liquid state is studied where we show that the state (which we call U(1)U(1)U(1)-Fermi liquid state) has Fermi-liquid like properties except that the quasi-particles are {\em not} adiabatically connected to bare fermions in the system and the state may not satisfy Luttinger theorem.
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