Platforms for the realization and characterization of Tomonaga-Luttinger liquids

TL;DR

This paper reviews the experimental platforms and theoretical understanding of Tomonaga-Luttinger liquids, emphasizing their role in describing one-dimensional quantum systems across various physical realizations.

Contribution

It provides a comprehensive overview of the experimental realization and characterization of TLLs, highlighting the validation of conformal field theory in real-world 1D quantum systems.

Findings

Experimental confirmation of TLL behavior in diverse platforms

Validation of conformal field theory for 1D quantum systems

Demonstration of quantum-critical TLL state governing many-body properties

Abstract

The concept of a Tomonaga-Luttinger liquid (TLL) has been established as a fundamental theory for the understanding of one-dimensional quantum systems. Originally formulated as a replacement for Landau's Fermi-liquid theory, which accurately predicts the behaviour of most 3D metals but fails dramatically in 1D, the TLL description applies to a even broader class of 1D systems,including bosons and anyons. After a certain number of theoretical breakthroughs, its descriptive power has now been confirmed experimentally in different experimental platforms. They extend from organic conductors, carbon nanotubes, quantum wires, topological edge states of quantum spin Hall insulators to cold atoms, Josephson junctions, Bose liquids confined within 1D nanocapillaries and spin chains. In the ground state of such systems, quantum fluctuations become correlated on all length scales, but, counter-intuitively, no long-range order exists. In this respect, this review will illustrate the validity of conformal field theory for describing real-world systems, establishing the boundaries for its application and, on the other side will discuss the spectacular demonstration of how the quantum-critical TLL state governs the properties of many-body systems in one dimension.