Anomalous reduction of the Lorenz ratio at the quantum critical point in YbAgGe

We report measurements of the electrical and thermal transport on the hexagonal heavy-fermion metal YbAgGe for temperatures $T\geq$ 40 mK and in magnetic fields $H\parallel ab$ up to 14 T. This distorted Kagome-lattice system displays a series of magnetic states and a quantum critical point at $H_c =4.5$ T. The Lorenz ratio $L(T)/L_0$ displays a marked reduction only close to $H_c$. A $T$-linear contribution below 120 mK, present at all different fields, allows to extrapolate the Lorenz ratio towards T=0. At the critical field this yields $L/L_0=0.92\pm 0.03$, suggesting a violation of the Wiedemann-Franz law due to strong inelastic scattering.