Néel orders, Haldane gap, and Kondo singlet phase in the anisotropic Kondo chain

The ground-state phase diagram of the Kondo chain with an anisotropic exchange is investigated. Four different phases are identified, two types of Néel phases, the Haldane phase, and the Kondo singlet phase. The boundaries between these phases in the strong coupling region are determined by mapping to effective models: the spin-1 Heisenberg model with single-ion anisotropy and the Ising model in a transverse magnetic field. It is shown that these transition lines extend to the weak-coupling limit and they are estimated by using the exact numerical diagonalization for a finite system.