Effect of external magnetic field on low-energy behavior of one-dimensional Heisenberg chain

Spin-in anisotropic Heisenberg chain in longitudinal external magnetic field is studied by traditional Jordan-Wigner transformation and bosonization method. In the presence of an external field, both Fermi velocity and Fermi momentum are changed, thus the bosonization procedure is also changed. The antiferromagnetic phase and paramagnetic phase are discussed and the dependence of ground state energy and magnetization on the field are calculated and depicted for some typical cases.