Uncovering Non-Fermi-Liquid Behavior in Hund Metals: Conformal Field Theory Analysis of an SU(2)×SU(3) Spin-Orbital Kondo Model

Abstract

Hund metals have attracted attention in recent years due to their unconventional superconductivity, which supposedly originates from non-Fermi-liquid (NFL) properties of the normal state. When studying Hund metals using dynamical mean-field theory, one arrives at a self-consistent "Hund impurity problem" involving a multiorbital quantum impurity with nonzero Hund coupling interacting with a metallic bath. If its spin and orbital degrees of freedom are screened at different energy scales, T sp < T orb , the intermediate energy window is governed by a novel NFL fixed point, whose nature had not yet been clarified. We resolve this problem by providing an analytical solution of a paradigmatic example of a Hund impurity problem, involving two spin and three orbital degrees of freedom. To this end, we combine a state-ofthe-art implementation of the numerical renormalization group, capable of exploiting non-Abelian symmetries, with a generalization of Affleck and Ludwig's conformal field theory (CFT) approach for multichannel Kondo models. We characterize the NFL fixed point of Hund metals in detail for a Kondo model with an impurity forming an SUð2Þ × SUð3Þ spin-orbital multiplet, tuned such that the NFL energy window is very wide. The impurity's spin and orbital susceptibilities then exhibit striking power-law behavior, which we explain using CFT arguments. We find excellent agreement between CFT predictions and numerical renormalization group results. Our main physical conclusion is that the regime of spinorbital separation, where orbital degrees of freedom have been screened but spin degrees of freedom have not, features anomalously strong local spin fluctuations: the impurity susceptibility increases as χ imp sp ∼ ω −γ , with γ > 1.

Is the orbital-selective Mott phase stable against interorbital hopping?

“…Assuming a divergent Σ hv ν for low frequencies, ∆ hv ν retains a finite value, independent of Σ hv ν . Combining this with the fact that a finite hybridization leads to a Fermi-liquid ground state in fairly general impurity models [11,[49][50][51][52], we find that, with A hv ∆,ν = k ( io k ) 2 A lt kν > 0, the Mott insulating state of the heavy orbital is unstable against interorbital hopping. In further DMFT iterations, a quasiparticle peak in the heavy orbital will form, and Σ hv ν will no longer diverge.…”

“…The impurity solution yielding g ν and Σ ν is determined by the hybridization ∆ ν with spectral weights A n ∆,ν = −Im ∆ n ν /π. In most cases [11,[49][50][51][52], a Fermi-liquid ground state is found if all A n ∆,ν are finite around ν = 0, while a Mott-insulating orbital requires a gapped A n ∆,ν .…”

Differentiating Hund from Mott physics in a three-band Hubbard-Hund model: Temperature dependence of spectral, transport, and thermodynamic properties

“…(1) using dynamical mean-field theory (DMFT) [4] combined with a state-of-the-art multi-band impurity solver, the fulldensity-matrix numerical renormalization group (fdm-NRG) [38,39], while fully exploiting the model's U(1) ch ×SU(2) spin ×SU(3) orb symmetry using the QSpace tensor library [40]. This approach has yielded valuable insights into the complex interplay of spin and orbital degrees of freedom before [7,20,22,29], because it delivers high-quality results directly on the real-frequency axes and for all physically relevant energies and temperatures. Details of the DMFT+fdmNRG method are described in Refs.…”

“…1(c) for H1). The incoherent regime is strongly particle-hole asymmetric in frequency space [20,22] and shows fractional powerlaw behavior [29,[41][42][43]. At zero temperature, the twostep SOS Kondo screening process is reflected in A(ω) in form of a two-tier QP peak on top of the broad incoherent background.…”

“…In Refs. [20,22,29] the focus has mainly been on zero-temperature results, while some finite-temperature results were published in Ref. [7].…”