Fermionic description of spin-gap states of antiferromagnetic Heisenberg   ladders in a magnetic field
  Employing the Jordan-Wigner transformation on a unique path and then making a mean-field treatment of the fermionic Hamiltonian, we semiquantitatively describe the spin-gap states of Heisenberg ladders in a field. The appearance of magnetization plateaux is clarified as a function of the number of legs. 
Hiromitsu Hori and Shoji Yamamoto