  We propose a skyrmion liquid state for the non-Fermi liquid (NFL) phase in
Ge-substituted YbRh$_{2}$Si$_{2}$, where skyrmions form their Fermi surface,
argued to result from the strongly coupled nature between skyrmions and
itinerant electrons. The fermionized skyrmion theory identifies the
antiferromagnetic (AF) transition with the Lifshitz transition, where the
quantum critical point (QCP) is characterized by the dynamical critical
exponent $z = 2$. Nonlocal interactions between skyrmions allow a critical line
above the AF QCP, which originates from the Kondo-coupling effect with
itinerant electrons. This critical line is described by the skyrmion liquid
state, which results in Landau damping for spin fluctuations, thus
characterized by $z = 3$. As a result, the Gruneisen ratio is predicted to
change from $\sim T^{-1}$ at the AF QCP to $\sim T^{-2/3}$ in the NFL phase.
