Quantum corrected phase diagram of holographic fermions

TL;DR

This paper investigates the phase diagram of strongly correlated electrons in two dimensions using holographic duality, revealing quantum corrections to electron star models and a first-order thermal phase transition to a charged black hole.

Contribution

It introduces a quantum many-body model of bulk fermion dynamics with WKB approximation, providing a quantum corrected phase diagram and new insights into phase transitions in holographic fermion systems.

Findings

Quantum corrected electron star with wavefunctions extended through AdS

First order thermal phase transition to charged AdS-RN black hole

Restoration of van der Waals type transition between phases

Abstract

We study the phases of strongly correlated electron systems in two spatial dimensions in the framework of AdS${}_4$/CFT${}_3$ correspondence. The AdS (gravity) model consists of a Dirac fermion coupled to electromagnetic field and gravity. To classify the ground states of strongly correlated electrons on the CFT side and to construct the full phase diagram of the system, we construct a quantum many-body model of bulk fermion dynamics, based on the WKB approximation to the Dirac equation. At low temperatures, we find a quantum corrected approximation to the electron star where the edge is resolved in terms of wavefunctions extended fully through AdS. At high temperatures, the system exhibits a {\em first} order thermal phase transition to a charged AdS-RN black hole in the bulk and the emergence of local quantum criticality on the CFT side. This change from the third order transition experienced by the semi-classical electron star restores the intuition that the transition between the critical AdS-RN liquid and the finite density Fermi system is of van der Waals liquid-gas type.