Itinerant Quantum Critical Point with Fermion Pockets and Hot Spots

Abstract

Metallic quantum criticality is among the central theme in the understanding of correlated electronic systems, and converging results between analytical and numerical approaches are still under calling. In this work, we develop state-of-art large scale quantum Monte Carlo simulation technique and systematically investigate the itinerant quantum critical point on a 2D square lattice with antiferromagnetic spin fluctuations at wavevector $\mathbf{Q}=(\pi,\pi)$ -- a problem that resembles the Fermi surface setup and low-energy antiferromagnetic fluctuations in high-Tc cuprates and other critical metals, which might be relevant to their non-Fermi-liquid behaviors. System sizes of $60\times 60 \times 320$ ($L \times L \times L_\tau$) are comfortably accessed, and the quantum critical scaling behaviors are revealed with unprecedingly high precision. We found that the antiferromagnetic spin fluctuations introduce effective interactions among fermions and the fermions in return render the bare bosonic critical point into a new universality, different from both the bare Ising universality class and the Hertz-Mills-Moriya RPA prediction. At the quantum critical point, a finite anomalous dimension $\eta\sim 0.125$ is observed in the bosonic propagator, and fermions at hot spots evolve into a non-Fermi-liquid. In the antiferromagnetically ordered metallic phase, fermion pockets are observed as energy gap opens up at the hot spots. These results bridge the recent theoretical and numerical developments in metallic quantum criticality and can be served as the stepping stone towards final understanding of the 2D correlated fermions interacting with gapless critical excitations.