Kondo Breakdown and Hybridization Fluctuations in the Kondo-Heisenberg Lattice

We study the deconfined quantum critical point of the Kondo-Heisenberg lattice in three dimensions using a fermionic representation for the localized spins. The mean-field phase diagram exhibits a zero temperature quantum critical point separating a spin liquid phase where the hybridization vanishes and a Kondo phase where it does not. Two solutions can be stabilized in the Kondo phase: namely, a uniform hybridization when the band masses of the conduction electrons and the spinons have the same sign, and a modulated one when they have opposite sign. For the uniform case, we show that above a very small temperature scale, the critical fluctuations associated with the vanishing hybridization have dynamical exponent $z=3$, giving rise to a resistivity that has a $T\log T$ behavior. We also find that the specific heat coefficient diverges logarithmically in temperature, as observed in a number of heavy fermion metals.

Figure 1

(a) $q$ dependence of ${\Pi }_{\mathrm{fc}}$ ($\alpha =0.01$ and $q^{*}/k_F=0.1$). Note differing scales for the $e\mathrm{\text{−}}e$ and $e\mathrm{\text{−}}h$ cases. (b) Quantum critical point as a function of $J_K$ and $J_H$ for the $e\mathrm{\text{−}}e$ ($q=0$) and $e\mathrm{\text{−}}h$ ($q=1.2q^{*}$) cases.

Figure 2

(a) Structure of $D_{\sigma }$ for the $e\mathrm{\text{−}}e$ case ($\alpha \ll 1$) at the QCP for positive frequencies. $z$ is the dynamical exponent in the various regions, which are delineated by the dashed lines, equal to $\alpha v_F(q^{*}\pm q)$ and $v_F(q^{*}\pm q)$. ${\omega }_{\mathrm{coll}}$ is the zero of $D_{\sigma }^{-1}$ in the $z=2$ regime (a propagating mode), and ${\Gamma }_q$ is the dispersion of the damped mode in the $z=3$ regime (maximum of the imaginary part of $D_{\sigma }$). Note the presence of energy scales $E^{*}\sim {10}^{-4}\alpha D$ and $E_X=\alpha v_F{q}^{*}\sim {10}^{-1}\alpha D$. (b) Phase diagram for the $e\mathrm{\text{−}}e$ case ($\alpha \ll 1$). Note the crossover from $z=2$ to $z=3$ behavior at $E^{*}$ (dotted line). The inset shows the phase diagram on a linear scale. The solid line is the crossover line in the Kondo phase, the dashed line the crossover line in the spin liquid phase.