Scaling and commensurate-incommensurate crossover for the d=2, z=2 quantum critical point of itinerant antiferromagnets

TL;DR

This paper investigates the extent of quantum critical scaling in the two-dimensional Hubbard model near a spin-density wave quantum critical point, revealing that scaling persists to high temperatures but is affected by incommensurate crossover effects.

Contribution

It provides the first detailed analysis of the quantum critical scaling range in the d=2, z=2 universality class using the Two-Particle Self-Consistent approach.

Findings

Quantum critical scaling extends to high temperatures.

Incommensurate crossover causes deviations from scaling.

Logarithmic corrections are present but do not prevent scaling.

Abstract

Quantum critical points exist at zero temperature, yet, experimentally their influence seems to extend over a large part of the phase diagram of systems such as heavy-fermion compounds and high-temperature superconductors. Theoretically, however, it is generally not known over what range of parameters the physics is governed by the quantum critical point. We answer this question for the spin-density wave to fermi-liquid quantum critical point in the two-dimensional Hubbard model. This problem is in the $d=2,z=2$ universality class. We use the Two-Particle Self-Consistent approach, which is accurate from weak to intermediate coupling, and whose critical behavior is the same as for the self-consistent-renormalized approach of Moriya. Despite the presence of logarithmic corrections, numerical results demonstrate that quantum critical scaling for the static magnetic susceptibility can extend up to very high temperatures but that the commensurate to incommensurate crossover leads to deviations to scaling.