Low Energy Behaviour of XXZ Antiferromagnetic Spin Chain

Zero temperature phase diagram of XXZ spin chain in external magnetic field is investigated at low energies using path integral approach.It has been shown by spin wave analysis and then by nonlinear sigma model transformation that below some critical field the system undergoes quantum Kosterlitz-Thouless phase transition.Above that critical field for low anisotropies the system is saturated while at strong anisotropy the system has Ising antiferromagnetic order.