We study the N´eel state of the spin 1 2 Heisenberg antiferromagnet model on hypercubic and triangular lattices, employing an auxiliary fermion representation for spin operators with Popov-Fedotov trick. The unphysical states are eliminated on each site by introducing an imaginary chemical potential. Working in local coordinate systems we obtain the free energy and the sublattice magnetization for both lattices in an unified manner. We show that exact treatment of the single occupancy constraint gives a significant effect at finite temperatures. | Communications in Physics, Vol. 22, No. 1 (2012), pp. 33-43 ´ NEEL STATE IN THE FERMIONIZED SPIN 21 HEISENBERG ANTIFERROMAGNET ON HYPERCUBIC AND TRIANGULAR LATTICES PHAM THI THANH NGA Water Resources University, 175 Tay Son, Hanoi NGUYEN TOAN THANG Institute of Physics, VAST Abstract. We study the N´eel state of the spin 12 Heisenberg antiferromagnet model on hypercubic and triangular lattices, employing an auxiliary fermion representation for spin operators with Popov-Fedotov trick. The unphysical states are eliminated on each site by introducing an imaginary chemical potential. Working in local coordinate systems we obtain the free energy and the sublattice magnetization for both lattices in an unified manner. We show that exact treatment of the single occupancy constraint gives a significant effect at finite temperatures. I. INTRODUCTION The fundamental problem in the theoretical investigation of spin systems is that spin operators satisfy neither Bose nor Fermi commutation relations, so one cannot use Wick’s theorem to construct a standard many body techniques. In order to avoid this difficulty various approaches to the study of spin systems have been suggested. One of the approaches is based upon representing operators in term of Bose or Fermi spin operators [1-2]. However, introduction of the auxiliary Bose or Fermi operators enlarges the Hilbert space in which these operators are acting. As a result, the unphysical states appear and should be excluded. In order to exclude these states one has to impose the constraint on bilinear combinations of Fermi or Bose operators. For example, for spin S = 21 the fermi operators introduce the spurious double occupied and empty states which must be freezed out. Unfortunately in general it is very difficult to take the constraint exactly into account and usually the local constraint is replaced with the global one, where the number of states is fixed only on an average for the whole system instead of being fixed .
