Hyperscaling violation at the Ising-nematic quantum critical point in two dimensional metals

TL;DR

This paper investigates hyperscaling violation at the Ising-nematic quantum critical point in two-dimensional metals, revealing a violation characterized by a specific exponent, using a controlled dimensional regularization approach.

Contribution

The study demonstrates hyperscaling violation with a specific exponent at the Ising-nematic critical point in 2D, employing a controlled regularization method.

Findings

Hyperscaling is violated with =1 in 2D.

Results are expected to extend to Fermi surfaces coupled to gauge fields in 2D.

The study uses a controlled dimensional regularization approach.

Abstract

Understanding optical conductivity data in the optimally doped cuprates in the framework of quantum criticality requires a strongly-coupled quantum critical metal which violates hyperscaling. In the simplest scaling framework, hyperscaling violation can be characterized by a single non-zero exponent $\theta$, so that in a spatially isotropic state in $d$ spatial dimensions, the specific heat scales with temperature as $T^{(d-\theta)/z}$, and the optical conductivity scales with frequency as $\omega^{(d-\theta-2)/z}$ for $\omega \gg T$, where $z$ is the dynamic critical exponent. We study the Ising-nematic critical point, using the controlled dimensional regularization method proposed by Dalidovich and Lee (Phys. Rev. B {\bf 88}, 245106 (2013)). We find that hyperscaling is violated, with $\theta =1$ in $d=2$. We expect that similar results apply to Fermi surfaces coupled to gauge fields in $d=2$.