Several heavy-fermion metals display a quantum phase transition from an antiferromagnetic metal to a heavy Fermi liquid. In some materials, however, recent experiments seem to find that the heavy Fermi liquid phase can be directly tuned into a non-Fermi liquid phase without apparent magnetic order. We analyze a candidate state for this scenario where the local moment system forms a spin liquid with gapless fermionic excitations. We discuss the thermal conductivity and spin susceptibility of this fractionalized state both in two and, in particular, three spatial dimensions for different temperature regimes. We derive a variational functional for the thermal conductivity and solve it with a variational ansatz dictated by Keldysh formalism. In sufficiently clean samples and for an appropriate temperature window, we find that thermal transport is dominated by the spinon contribution which can be detected by a characteristic maximum in the Wiedemann-Franz ratio. For the spin susceptibility, the conduction electron Pauli paramagnetism is much smaller than the spinon contribution whose temperature dependence in three dimensions is logarithmically enhanced as compared to the Fermi liquid result.

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Thermodynamic and transport signatures of a fractionalized Fermi liquid

based on the random phase approximation has been performed for multi-scale quantum criticality, an extension to an Eliashberg framework was claimed to be far from triviality in respect that the self-energy correction beyond the random phase approximation, which originates from scattering with z = 3 longitudinal fluctuations, changes the dynamical exponent z = 2 in the transverse mode, explicitly demonstrated in nematic quantum criticality. A novel ingredient of the present study is to introduce an anomalous self-energy associated with the spin-flip channel. Such an anomalous selfenergy turns out to be essential for self-consistency of the Eliashberg framework in the multi-scale quantum critical point because this off diagonal self-energy cancels the normal self-energy exactly in the low energy limit, preserving the dynamics of both z = 3 longitudinal and z = 2 transverse modes. This multi-scale quantum criticality is consistent with that in a perturbative analysis for the nematic quantum critical point, where a vertex correction in the fermion bubble diagram cancels a singular contribution due to the self-energy correction, maintaining the z = 2 transverse mode. We also claim that this off diagonal self-energy gives rise to an artificial electric field in the energymomentum space in addition to the Berry curvature. We discuss the role of such an anomalous self-energy in the anomalous Hall conductivity. PACS numbers:

Nambu-Eliashberg theory for multiscale quantum criticality: Application to ferromagnetic quantum criticality in the surface of three-dimensional topological insulators

We find that the Kondo effect results in a new universality class for an antiferromagnetic (AF) quantum critical point (QCP) in the heavy fermion quantum transition, described by deconfined bosonic spinons with the dynamical exponent $z=3$ We show that the thermodynamics and transport of the $z=3$ AF QCP are consistent with the well-known non-Fermi liquid physics such as the divergent Gr\"uneisen ratio with an exponent $2/3$ and temperature-linear resistivity We propose that the hallmark of the Kondo-driven AF QCP is a uniform spin susceptibility that diverges with an exponent $2/3$, remarkably consistent with the experimental observations for ${\mathrm{YbRh}}_{2}{\mathrm{Si}}_{2}$

z = 3 Antiferromagnetic Quantum Criticality Driven by the Kondo Effect

We predict that long-range interactions give rise to anisotropy in the electrical resistivity of Weyl metals at low temperatures, where the electrical resistivity becomes much reduced when electric fields are applied to the direction of the momentum vector to connect two paired Weyl points. Performing the renormalization group analysis, we find that the distance between two Weyl points becomes enhanced logarithmically at low temperatures although the coupling constant of such interactions vanishes inverse-logarithmically. Considering the Adler-Bell-Jackiw anomaly, scattering between these two Weyl points becomes suppressed to increase electrical conductivity in the ``longitudinal'' direction, counter intuitive in the respect that interactions are expected to reduce metallicity. We also propose that the anomalous contribution in the Hall effect shows the logarithmic enhancement as a function of temperature, originating from the fact that the anomalous Hall coefficient turns out to be proportional to the distance between two paired Weyl points. Correlations with topological constraints allow unexpected and exotic transport properties.

Interplay between interaction and chiral anomaly: Anisotropy in the electrical resistivity of interacting Weyl metals

We develop the quantum Boltzman equation approach for the Kondo breakdown quantum critical point, involved with two bands for conduction electrons and localized fermions. Particularly, the role of vertex corrections in transport is addressed, crucial for non-Fermi liquid transport of temperature linear dependence. Only one band of spinons may be considered for scattering with gauge fluctuations, and their associated vertex corrections are introduced in the usual way, where divergence of self-energy corrections is cancelled by that of vertex corrections, giving rise to the physically meaningful result in the gauge invariant expression for conductivity. On the other hand, two bands should be taken into account for scattering with hybridization excitations, giving rise to coupled quantum Boltzman equations. We find that vertex corrections associated with hybridization fluctuations turn out to be irrelevant due to heavy mass of spinons in the so called decoupling limit, consistent with the diagrammatic approach showing the non-Fermi liquid transport.

Quantum Boltzman equation study for the Kondo breakdown quantum critical point

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Quantum Boltzman equation study for the Kondo breakdown quantum critical point