Lectures on holographic non-Fermi liquids and quantum phase transitions

TL;DR

This paper reviews how gauge/gravity duality can be used to study non-Fermi liquids and quantum phase transitions in holographic systems, highlighting the role of charged black holes and semi-local quantum liquids.

Contribution

It introduces a framework for analyzing non-Fermi liquids and quantum criticality using holography, emphasizing the semi-local quantum liquid phase and its implications.

Findings

Identification of Fermi surface properties in holographic models

Observation of instabilities leading to scalar operator condensation

Discovery of semi-local quantum liquids as a universal intermediate phase

Abstract

In these lecture notes we review some recent attempts at searching for non-Fermi liquids and novel quantum phase transitions in holographic systems using gauge/gravity duality. We do this by studying the simplest finite density system arising from the duality, obtained by turning on a nonzero chemical potential for a U(1) global symmetry of a CFT, and described on the gravity side by a charged black hole. We address the following questions of such a finite density system: 1. Does the system have a Fermi surface? What are the properties of low energy excitations near the Fermi surface? 2. Does the system have an instability to condensation of scalar operators? What is the critical behavior near the corresponding quantum critical point? We find interesting parallels with those of high T_c cuprates and heavy electron systems. Playing a crucial role in our discussion is a universal intermediate-energy phase, called a "semi-local quantum liquid", which underlies the non-Fermi liquid and novel quantum critical behavior of a system. It also provides a novel mechanism for the emergence of lower energy states such as a Fermi liquid or a superconductor.