Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo

Over the last decade there has been a surge of activity in studying various quantum phenomena via electronic `constructor models' that lack the fermion sign problem. Of note are constructor models of quantum phase transitions in metallic systems, where it is easier to find such microscopic models due to the notion of universality. However, this agenda has been hampered due to the expensive scaling with system size of Determinant Quantum Monte Carlo, making it difficult to convincingly extract long-wavelength information from the critical theory. In this talk I will introduce a Hybrid Monte Carlo (HMC) algorithm with a novel auto-tuning procedure. We apply this method to the O(3) spin-fermion model, a minimal model of the onset of antiferromagnetic order in a two-dimensional metal. Our method allows us to study unprecedentedly large systems of 80×80 sites, even at criticality. To characterize the universality class of the quantum critical point, we extract the scaling exponents and functional form of the static and zero-momentum dynamical spin susceptibility. We find a strong violation of the Hertz-Millis form, contrary to all previous results. The form that we do observe provides strong evidence that the universal scaling is actually governed by the fixed point of [Phys. Rev. X 7, 021010 (2017)], even away from perfect hot-spot nesting. Our results suggest that controlled analytical calculations of the critical theory near perfect hot-spot nesting can be used to make qualitatively correct predictions at larger nesting angles of other observables. Additionally, the HMC method we introduce is generic and can be used to study other fermionic models of quantum criticality, where there is a strong need to simulate large systems.