Hierarchy of energy scales in an O(3) symmetric antiferromagnetic quantum critical metal: A Monte Carlo study

Abstract

We present numerically exact results from sign-problem free quantum Monte Carlo simulations for a spinfermion model near an O(3) symmetric antiferromagnetic (AFM) quantum critical point. We find a hierarchy of energy scales that emerges near the quantum critical point. At high energy scales, there is a broad regime characterized by Landau-damped order parameter dynamics with dynamical critical exponent z = 2, while the fermionic excitations remain coherent. The quantum critical magnetic fluctuations are well described by Hertz-Millis theory, except for a T −2 divergence of the static AFM susceptibility. This regime persists down to a lower energy scale, where the fermions become overdamped and concomitantly, a transition into a d−wave superconducting state occurs. These findings resemble earlier results for a spin-fermion model with easy-plane AFM fluctuations of an O(2) SDW order parameter, despite noticeable differences in the perturbative structure of the two theories. In the O(3) case, perturbative corrections to the spin-fermion vertex are expected to dominate at an additional energy scale, below which the z = 2 behavior breaks down, leading to a novel z = 1 fixed point with emergent local nesting at the hot spots [Schlief et al., PRX 7, 021010 (2017)]. Motivated by this prediction, we also consider a variant of the model where the hot spots are nearly locally nested. Within the available temperature range in our study (T ≥ E F 200), we find substantial deviations from the z = 2 Hertz-Millis behavior, but no evidence for the predicted z = 1 criticality. arXiv:2001.00586v3 [cond-mat.str-el]

Normal State Properties of Quantum Critical Metals at Finite Temperature

“…We believe that our results imply that the QMC data are a validation of, rather than a challenge to, the applicability of ET to quantum-critical models of interacting electrons. We note that a recent additional QMC calculation for the spinfermion model [46], using a different microscopic model from the one in our detailed comparison, also evinces selfenergy behavior consistent with MET.…”

“…The validity of the effective ET at a QCP has recently been tested in a series of sign-free quantum Monte Carlo (QMC) simulations of both the spin-fermion and Isingnematic models [11,[39][40][41][42][43][44][45][46]. Such simulations are numerical experiments that test effective models of quantumcritical metals [45,47,48].…”

Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data

“…Although this paper mainly focuses on the itinerant ferromagnetism QCP as an example to demonstrate the physics, the technique is universal and can be easily generalized to other itinerant QCPs, such as nematic and AFM-QCPs 49,52,53,56 . Furthermore, this technique can also be used to explore the predicted non-trivial effects from higher-order corrections 16,25,27,29,35,76 , and thus open up a pathway towards a full understanding about this challenging subject of NFLs.…”

“…In particular, it has been found that designer models of fermion-boson models offer a pathway to access fermionic QCPs while avoiding the notorious sign problem in large-scale quantum Monte Carlo (QMC) simulations. Such models have been implemented in several simulations, studying nematic 49,50 , ferromagnetic 51 , antiferromagnetic [52][53][54][55][56] , gauge field [57][58][59][60][61][62] , and Yukawa-SYK-type 41 QCPs. The focusing on a particular soft boson offers an unbiased numerical test for either a Q = 0 or a finite Q analytical theory of metallic quantum criticality.…”

Fast and stable determinant quantum Monte Carlo

“…Due to their intrinsic correlations they feature rich phase diagrams which can not be captured by purely classical nor non-interacting theories. Especially at the lowest temperatures, quantum mechanical fluctuations driven by Heisenberg's uncertainty principle become relevant and lead to novel phases of matter like superconductivity and states beyond the Fermi liquid paradigm [1,2]. Because of the presence of interactions, predicting microscopic and thermodynamic properties of fermion many-body systems is inherently difficult.…”