Geometry and topological order in the non-relativistic Luttinger liquid

TL;DR

This paper reveals that non-relativistic Luttinger liquids possess a form of topological order beyond spin-charge separation, detectable through non-local correlation functions, expanding the understanding of quantum states in condensed matter physics.

Contribution

It introduces the concept of topological order in non-relativistic Luttinger liquids, extending the traditional Tomonaga-Luttinger theory.

Findings

Luttinger liquids exhibit topological order beyond spin-charge separation.

Non-local correlation functions can reveal this topological order.

The results connect condensed matter physics with lattice gauge theory concepts.

Abstract

We demonstrate that the notion of spin-charge separation as follows from the Tomonaga-Luttinger theory of relativistic fermions does not suffice to completely specify the Luttinger liquid state associated with the fermions of condensed matter physics. The latter carries in addition a form of topological order which can be made visible using non-local correlation functions familiar from lattice gauge theory.