We revisit Stoner instability, an old problem but in a modern point of view. An idea is to extract out dynamics of directional fluctuations of spins explicitly, resorting to the CP
1 representation and integrating over their amplitude fluctuations. As a result, we derive an effective field theory for ferromagnetic quantum phase transitions in terms of bosonic spinons and fermionic holons. We show that this effective field theory reproduces overdamped spin dynamics in a paramagnetic Fermi liquid and magnon spectrum in a ferromagnetic Fermi liquid. An interesting observation is that the velocity of spinons becomes zero, approaching the ferromagnetic quantum critical point, which implies emergence of local quantum criticality. Based on this scenario, we predict the
ω/T scaling behavior near ferromagnetic quantum criticality beyond the conventional scenario of the weak-coupling approach.
A general understanding of quantum phase transitions in strongly correlated materials is still lacking. By exploiting a cutting-edge quantum many-body approach, the dynamical vertex approximation, we make important progress, determining the quantum critical properties of the antiferromagnetic transition in the fundamental model for correlated electrons, the Hubbard model in three dimensions. In particular, we demonstrate that-in contradiction to the conventional Hertz-Millis-Moriya theory-its quantum critical behavior is driven by the Kohn anomalies of the Fermi surface, even when electronic correlations become strong.
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 behavior and superconducting phase. A minimal model for this transition is the O(3) spin-fermion model. Despite many efforts, a definitive characterization of its universal properties is still lacking. Here, we numerically study the 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 × 80 sites. We find a strong violation of the Hertz-Millis form, contrary to all previous numerical 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.
The interplay of magnetic and superconducting fluctuations in two-dimensional systems with van Hove singularities in the electronic spectrum is considered within the functional renormalization-group (fRG) approach. While the fRG flow has to be stopped at a certain minimal temperature
TRGmin, we study temperature dependence of magnetic and superconducting susceptibilities below
TRGmin to obtain the crossover temperatures to the regime with strong magnetic and superconducting fluctuations. Near half filling we obtain the largest crossover temperature, corresponding to a regime with strong commensurate magnetic fluctuations, which is replaced by a regime with strong incommensurate fluctuations further away from half filling. With further decreasing density the system undergoes quantum phase transition from incommensurate to paramagnetic phase. Similarly to results of Hertz-Moriya-Millis approach, the temperature dependence of the inverse (incommensurate) magnetic susceptibility at the magnetic quantum-critical point is found almost linear in temperature.
Emergence of localized magnetic moments in the vicinity of a metal-insulator transition is a non-perturbative phenomenon beyond the description based on the perturbative theoretical framework. Resorting to a recently developed theoretical device called dimensional regularization for the Fermi-surface problem, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Assuming that the spinon Fermi surface can be destabilized across the spin-liquid Mott quantum critical point, we show that such itinerant spinons become localized to result in localized magnetic moments near the spin-liquid Mott quantum critical point. The role of such emergent moments in non-Fermi liquid physics reveals the nature of spin-liquid Mott quantum criticality as novel local quantum criticality, where critical charge dynamics belongs to the inverted XY universality class and critical spin dynamics conforms to a locally critical universality class.
We study the dynamics of critical spin fluctuations and hot electrons at the metallic antiferromagnetic quantum critical points with
Z2 and O(2) spin symmetries, building on earlier works on the O(3) symmetric theory. The interacting theories in
2+1 dimensions are approached from
3+1-dimensional theories in the $\ensuremath{\epsilon}$ expansion that tunes the codimension of Fermi surface as a control parameter. The low-energy physics of the
Z2 and O(2) theories qualitatively differ from each other and also from that of the O(3) theory. The difference is caused by higher-order quantum corrections beyond the one-loop order that are important even to the leading order in $\ensuremath{\epsilon}$. The naive loop expansion breaks down due to dynamical quenching of kinetic energy: the speed of the collective mode (
c) and the Fermi velocity perpendicular to the magnetic ordering vector (
v) become vanishingly small at low energies. What sets the three theories apart is the hierarchy that emerges between the quenched kinetic terms. At the infrared fixed point,
c/v becomes 0, 1, and $\ensuremath{\infty}$ in the
Z2, O(2), and O(3) theories, respectively. At intermediate energy scales, the slow renormalization group (RG) flows of
c and
v toward their fixed point values create approximate scale invariance controlled by approximate marginal parameters. The manifold of those quasifixed points and the RG flow therein determines crossovers from scaling behaviors with transient critical exponents at intermediate energy scales to the universal scaling in the low-energy limit. If the symmetry group is viewed as a tuning parameter, then the O(2) theory corresponds to a multicritical point which has one additional quasimarginal parameter than the other two theories.