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arXiv:0811.3767

On Field-Induced Quantum Criticality in YbRh_{2}Si_[2}

M. S. Laad

Published Nov 23, 2008• 0 citations
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Abstract

The quantum critical point (QCP) in $YbRh_{2}Si_{2}$ is an enigma for the itinerant view of QCP. In an alternative view, this QCP is intimately linked to the selective Mott localization of the heavy $f$ electrons. Following a perusal of this unusual QCP, I study an Extended Periodic Anderson Model (EPAM) within DMFT. A quantum phase transition (FQPT), accompanied by a rapid change in the Fermi volume, is found near the quantum-critical end-point of the selective Mott transition in the $f$-electron sector. The theory accounts for a wide range of unusual, singular non-Fermi liquid features exhibited at this QCP in $YbRh_{2}Si_{2}$ in a natural way.

DOI
10.48550/arxiv.0811.3767

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The quantum critical point (QCP) in YbRh2Si2YbRh_{2}Si_{2}YbRh2​Si2​ is an enigma for the itinerant view of QCP. In an alternative view, this QCP is intimately linked to the selective Mott localization of the heavy fff electrons. Following a perusal of this unusual QCP, I study an Extended Periodic Anderson Model (EPAM) within DMFT. A quantum phase transition (FQPT), accompanied by a rapid change in the Fermi volume, is found near the quantum-critical end-point of the selective Mott transition in the fff-electron sector. The theory accounts for a wide range of unusual, singular non-Fermi liquid features exhibited at this QCP in YbRh2Si2YbRh_{2}Si_{2}YbRh2​Si2​ in a natural way.
We study the quantum phase transition in f-electron systems as a quantum Lifshitz transition driven by selective-Mott localization in a realistic extended Anderson lattice model. Using dynamical mean-field theory (DMFT), we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau-Fermi liquid from ordered phase(s). This non-Fermi liquid state arises from a lattice orthogonality catastrophe originating from orbital-selective Mott localization. Fermi surface reconstruction occurs via the interplay between and penetration of the Green function zeros to the poles, leading to violation of Luttinger's theorem in the strange metal. We show how this naturally leads to scale-invariant responses in transport. Thus, our work represents a specific DMFT realization of the hidden-FL and FL* theories, and holds promise for the study of 'strange' metal phases in quantum matter.
We study the quantum phase transition in f -electron systems as a quantum Lifshitz transition driven by selective Mott localization in a realistic extended Anderson lattice model.Using DMFT, we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau-Fermi liquid from ordered phase(s).Fermi surface reconstruction occurs via the interplay between, and penetration of the Green function zeros to the poles, leading to violation of Luttinger's theorem in the selective-Mott phase .We show how this naturally leads to scale-invariant responses in transport.Our work is represents a specific (DMFT) realization of the hidden-FL and FL * theories, and holds promise for study of "strange" metal phases in quantum matter.
We show that when there is a sudden transition from a small to a large Fermi surface at a field-induced quantum critical point---similar to what may have been observed in some heavy-fermion compounds---an additional term has to be taken into account in the Luttinger-Friedel sum rule. We calculate this additional term for a local model which has a field-induced quantum critical point (QCP) and show that it changes abruptly at the transition, such that it satisfies a generalized Luttinger-Friedel sum rule on each side of the transition, and characterizes the two Fermi-liquid phases separated by the QCP as a discrete (topological) index.
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Local quantum criticality in itinerant fermion systems has been extensively investigated through the soft-gap Anderson impurity model, wherein a localized, correlated impurity hybridizes with a broad conduction band with a singular, ${|\ensuremath{\omega}|}^{r}$, density of states. However, lattice models hosting quantum critical points (QCPs) do not appear to have such a spectrum emerging at the QCP. In this work, we report the emergence of such a singular form of the density of states in a three-orbital lattice model, within dynamical mean field theory, precisely at a quantum critical point, separating a gapless, Fermi liquid (FL) metallic phase from a gapped, Mott insulating phase. A temperature-dependent exponent, $\ensuremath{\alpha}$, defined using the corresponding Matsubara self-energy, is found to vary from +1+1+1 deep in the FL regime, to $\ensuremath{-}1$ in the Mott insulator regime. Interestingly, we find that $\ensuremath{\alpha}$ becomes temperature-independent, and hence isosbestic, precisely at the QCP. The isosbestic exponent is shown to lead to an emergent soft-gap spectrum, ${|\ensuremath{\omega}|}^{r}$, at the QCP, where $r=|{\ensuremath{\alpha}}_{\mathrm{iso}}|$. We discuss the implications of our findings for non-Fermi-liquid behavior in the quantum critical region of the phase diagram.
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.