Neutral Order Parameters in Metallic Criticality in d=2+1 from a Hairy Electron Star

TL;DR

This paper uses holography to study quantum phase transitions involving neutral order parameters in a (2+1)-dimensional metallic system at zero temperature, revealing novel critical behavior and phase structures.

Contribution

It demonstrates the emergence of neutral scalar hair in the electron star background, indicating a quantum phase transition with variable dynamical critical exponent and explores finite temperature effects.

Findings

Neutral scalar hair indicates a quantum phase transition.

Different phases across the transition have distinct dynamical critical exponents.

Finite temperature transitions are second-order.

Abstract

We use holography to study the spontaneous condensation of a neutral order parameter in a (2+1)-dimensional field theory at zero-temperature and finite density, dual to the electron star background of Hartnoll and Tavanfar. An appealing feature of this field theory is the emergence of an IR Lifshitz fixed-point with a finite dynamical critical exponent $z$, which is due to the strong interaction between critical bosonic degrees of freedom and a finite density of fermions (metallic quantum criticality). We show that under some circumstances the electron star background develops a neutral scalar hair whose holographic interpretation is that the boundary field theory undergoes a quantum phase transition, with a Berezinski-Kosterlitz-Thouless character, to a phase with a neutral order parameter. Including the backreaction of the bulk neutral scalar on the background, we argue that the two phases across the quantum critical point have different $z$, a novelty that exists in certain quantum phase transitions in condensed matter systems. We also analyze the system at finite temperature and find that the phase transition becomes, as expected, second-order. Embedding the neutral scalar into a higher form, a variety of interesting phases could potentially be realized for the boundary field theory. Examples which are of particular interest to condensed matter physics include an antiferromagnetic phase where a vector condenses and break the spin symmetry, a quadrupole nematic phase which involves the condensation of a symmetric traceless tensor breaking rotational symmetry, or different phases of a system with competing order parameters.