Phase Transitions in the Symmetric Kondo Lattice Model in Two and Three Dimensions

We present an application of high-order series expansion in the coupling constants for the ground state properties of correlated lattice fermion systems. Expansions have been generated up to order $(t/J)^{14}$ for $d=1$ and $(t/J)^8$ for $d=2,\ 3$ for certain properties of the symmetric Kondo lattice model. Analyzing the susceptibility series, we find evidence for a continuous phase transition from the ``spin liquid'' phase characteristic of a ``Kondo Insulator'' to an antiferromagnetically ordered phase in dimensions $d\ge2$ as the antiferromagnetic Kondo coupling is decreased. The critical point is estimated to be at $(t/J)_c\approx0.7$ for square lattice and $(t/J)_c\approx0.5$ for simple-cubic lattice.