Bilocal quantum criticality

TL;DR

This paper studies a 2+1D conformal gauge theory with long-range temporal interactions, revealing a strongly-coupled quantum critical point with linear specific heat behavior relevant to cuprate superconductors.

Contribution

It introduces a large N_h expansion for a SU(2) gauge theory with adjoint Higgs fields, uncovering a new quantum critical point with unique scaling properties.

Findings

Identifies a strongly-coupled fixed point with dynamic critical exponent z > 1.

Shows the entropy obeys hyperscaling despite non-trivial critical behavior.

Finds the specific heat is linear in temperature with an enhanced coefficient near criticality.

Abstract

We consider 2+1 dimensional conformal gauge theories coupled to additional degrees of freedom which induce a spatially local but long-range in time $1/(\tau-\tau')^2$ interaction between gauge-neutral local operators. Such theories have been argued to describe the hole-doped cuprates near optimal doping. We focus on a SU(2) gauge theory with $N_h$ flavors of adjoint Higgs fields undergoing a quantum transition between Higgs and confining phases: the $1/(\tau-\tau')^2$ interaction arises from a spectator large Fermi surface of electrons. The large $N_h$ expansion leads to an effective action containing fields which are bilocal in time but local in space. We find a strongly-coupled fixed point at order $1/N_h$, with dynamic critical exponent $z > 1$. We show that the entropy preserves hyperscaling, but nevertheless leads to a linear in temperature specific heat with a co-efficient which has a finite enhancement near the quantum critical point.