  A recently developed numerical method, entanglement perturbation theory
(EPT), is used to study the antiferromagnetic Heisenberg spin chains with
z-axis anisotropy $\lambda$ and magnetic field B. To demonstrate the accuracy,
we first apply EPT to the isotropic spin-1/2 antiferromagnetic Heisenberg
model, and find that EPT successfully reproduces the exact Bethe Ansatz results
for the ground state energy, the local magnetization, and the spin correlation
functions (Bethe ansatz result is available for the first 7 lattice
separations). In particular, EPT confirms for the first time the asymptotic
behavior of the spin correlation functions predicted by the conformal field
theory, which realizes only for lattice separations larger than 1000. Next,
turning on the z-axis anisotropy and the magnetic field, the 2-spin and 4-spin
correlation functions are calculated, and the results are compared with those
obtained by Bosonization and density matrix renormalization group methods.
Finally, for the spin-1 antiferromagnetic Heisenberg model, the ground state
phase diagram in $\lambda$ space is determined with help of the Roomany-Wyld RG
finite-size-scaling. The results are in good agreement with those obtained by
the level-spectroscopy method.
