Quantum critical properties of a metallic spin density wave transition

TL;DR

This study uses quantum Monte Carlo simulations to explore the quantum critical behavior of spin-density wave transitions in a metallic system, revealing deviations from traditional theories and their impact on superconductivity and quasiparticle properties.

Contribution

It provides the first numerically exact analysis of SDW quantum criticality in a sign-problem-free model, highlighting discrepancies with Hertz-Millis theory and its effects on fermionic quasiparticles.

Findings

Critical dynamics follow z=2 but deviate from predicted temperature dependence.

Critical SDW fluctuations induce a dome-shaped superconducting phase.

Non-Fermi liquid behavior emerges near hot spots above Tc.

Abstract

We report on numerically exact determinantal quantum Monte Carlo simulations of the onset of spin-density wave (SDW) order in itinerant electron systems captured by a sign-problem-free two-dimensional lattice model. Extensive measurements of the SDW correlations in the vicinity of the phase transition reveal that the critical dynamics of the bosonic order parameter are well described by a dynamical critical exponent z = 2, consistent with Hertz-Millis theory, but are found to follow a finite-temperature dependence that does not fit the predicted behavior of the same theory. The presence of critical SDW fluctuations is found to have a strong impact on the fermionic quasiparticles, giving rise to a dome-shaped superconducting phase near the quantum critical point. In the superconducting state we find a gap function that has an opposite sign between the two bands of the model and is nearly constant along the Fermi surface of each band. Above the superconducting $T_c$ our numerical simulations reveal a nearly temperature and frequency independent self energy causing a strong suppression of the low-energy quasiparticle spectral weight in the vicinity of the hot spots on the Fermi surface. This indicates a clear breakdown of Fermi liquid theory around these points.