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

Abstract

A key component of the phase diagram of many iron-based superconductors and electron-doped cuprates is believed to be a quantum critical point (QCP), delineating the onset of antiferromagnetic spin-density wave order in a quasi-two-dimensional metal. The universality class of this QCP is believed to play a fundamental role in the description of the proximate non-Fermi liquid and superconducting phases. A minimal model for this transition is the $\mathrm{O}(3)$ spin-fermion model. Despite many efforts, a definitive characterization of its universal properties is still lacking. Here, we numerically study the $\mathrm{O}(3)$ spin-fermion model and extract the scaling exponents and functional form of the static and zero-momentum dynamical spin susceptibility. We do this using a Hybrid Monte Carlo (HMC) algorithm with a novel auto-tuning procedure, which allows us to study unprecedentedly large systems of $80\times 80$ sites. We find a strong violation of the Hertz-Millis form, contrary to all previous results. Furthermore, the form that we do observe provides good evidence that the universal scaling is actually governed by the analytically tractable fixed point discovered near perfect ``hot-spot'" nesting, even for a larger nesting window. Our predictions can be directly tested with neutron scattering. 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.

16 pages, 9 figures (main text) + 8 pages, 10 figures (appendix)

References in corpus (15)

• High-temperature superconductivity in iron-based materials
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Is graphene in vacuum an insulator?
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• Quantum Critical Behaviour in a Graphene-like Model
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• A simple fermionic model of deconfined phases and phase transitions
• Quasi-Local Strange Metal
• Bipolaronic high-temperature superconductivity
• Monte-Carlo simulation of the tight-binding model of graphene with partially screened Coulomb interactions
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Superconductivity, charge density wave, and supersolidity in flat bands with tunable quantum metric
• Quantum critical properties of a metallic spin density wave transition
• Fast and scalable quantum Monte Carlo simulations of electron-phonon models
• Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions

Cited by in corpus (10)

• Localization of overdamped bosonic modes and transport in strange metals
• Stable computation of entanglement entropy for 2D interacting fermion systems
• Robust Fermi liquid instabilities in sign problem-free models
• Strange metals and planckian transport in a gapless phase from spatially random interactions
• Quantum Monte Carlo for Gauge Fields and Matter without the Fermion Determinant
• Interaction-enhanced nesting in Spin-Fermion and Fermi-Hubbard models
• Emergence of curved momentum-spacetime and its effect on the cyclotron motion in the antiferromagnetic quantum critical metal
• Scalable hybrid quantum Monte Carlo simulation of U(1) gauge field coupled to fermions on GPU
• Dynamical kinetic energy quenching in the antiferromagnetic quantum critical metals
• Staggered spin susceptibility at a two-dimensional antiferromagnetic quantum critical point