Holographic quantum liquids in 1+1 dimensions

TL;DR

This paper explores holographic models of 1+1 dimensional quantum liquids, revealing unique features like a dissipationless zero sound mode and analyzing spectral functions, contributing to understanding strongly correlated systems in low dimensions.

Contribution

It introduces a holographic model for 1+1D quantum liquids with a probe D3 brane, analyzing zero sound modes and spectral functions, and discusses implications for the Luttinger conjecture.

Findings

Discovery of a dissipationless zero sound mode in 1+1D holographic liquids

Analysis of spectral functions and quasinormal modes in the model

Insights into boundary term subtleties unique to 1+1 dimensions

Abstract

In this paper we initiate the study of holographic quantum liquids in 1+1 dimensions. Since the Landau Fermi liquid theory breaks down in 1+1 dimensions, it is of interest to see what holographic methods have to say about similar models. For theories with a gapless branch, the Luttinger conjecture states that there is an effective description of the physics in terms of a Luttinger liquid which is specified by two parameters. The theory we consider is the defect CFT arising due to a probe D3 brane in the AdS Schwarzschild planar black hole background. We turn on a fundamental string density on the worldvolume. Unlike higher dimensional defects, a persistent dissipationless zero sound mode is found. The thermodynamic aspects of these models are considered carefully and certain subtleties with boundary terms are explained which are unique to 1+1 dimensions. Spectral functions of bosonic and fermionic fluctuations are also considered and quasinormal modes are analysed. A prescription is given to compute spectral functions when there is mixing due to the worldvolume gauge field. We comment on the Luttinger conjecture in the light of our findings.