Fermi-Surface Reconstruction without Breakdown of Kondo Screening at the Quantum Critical Point

Motivated by recent Hall-effect experiment in ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$, we study ground state properties of a Kondo lattice model in a two-dimensional square lattice using variational Monte Carlo method. We show that there are two types of phase transition, an antiferromagnetic transition and a topological one (Fermi-surface reconstruction). In a wide region of parameters, these two transitions occur simultaneously without the breakdown of Kondo screening, accompanied by a discontinuous change of the Hall coefficient. This result is consistent with the experiment and gives a novel theoretical picture for the quantum critical point in heavy-fermion systems.

Figure 1

Fermi surfaces and band dispersions of the four different variational states considered in this Letter. (a) paramagnetic metal, (b) ${\mathrm{AF}}_h$, (c) ${\mathrm{AF}}_e$ and (d) ${\mathrm{AF}}_S$.

Figure 2

Ground state phase diagram in the $J\mathrm{\text{−}}{n}_c$ plane obtained in VMC. Solid lines ($J_{c,\mathrm{FS}}$ and $J_{c,\mathrm{AF}+\mathrm{FS}}$) represent the first-order phase transition and the dotted line ($J_{c,\mathrm{AF}}$) represents the second-order one.

Figure 3

Energy difference of each state compared with the PM state for (a) $n_c=0.9375$ and (b) $n_c=0.8125$. The error bars are on the order of ${10}^{-4}$ and are not shown here.