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

Understand

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.