Non-Fermi Liquid Behavior in a Disordered Kondo Alloy Model

Abstract

We study a mean-field model of a Kondo alloy using numerical techniques and analytic approximations. In this model, randomly distributed magnetic impurities interact with a band of conduction electrons and have a residual RKKY coupling of strength $J$. This system has a quantum critical point at $J=J_c\sim T_K^0$, the Kondo scale of the problem. The $T$ dependence of the spin susceptibility near the quantum critical point is singular with $\chi (0)-\chi (T)\propto T^{\gamma }$ and non-integer $\gamma$. At $J_c$, $\gamma =3/4$. For $J\lesssim J_c$ there are two crossovers with decreasing $T$, first to $\gamma =3/2$ and then to $\gamma =2$, the Fermi-liquid value. The dissipative part of the time-dependent susceptibility ${\chi }^{\prime \prime }(\omega )\propto \omega$ as $\omega \to 0$ except at the quantum critical point where we find ${\chi }^{\prime \prime }(\omega )\propto \sqrt{\omega }$. The characteristic spin-fluctuation energy vanishes at the quantum critical point with ${\omega }_{\mathrm{sf}}\sim (1-J/J_c)$ for $J\lesssim J_c$, and ${\omega }_{\mathrm{sf}}\propto T^{3/2}$ at the critical coupling.

22 pages, 8 figures. Minor changes. References added. Accepted by Phys. Rev. B

References in corpus (1)

• Dynamics of the Ising Spin-Glass Model in a Transverse Field

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