A field theoretical description of states with different orbitals for different spins

Abstract

AbstractA field theoretical formulation is given for the method of different orbitals for different spins (DODS). For an infinite system DODS describes an antiferromagnetic state and to account for this spin ordering a Gorkov‐type of factorization is introduced. A corresponding gap equation is derived, where a non‐zero solution indicates the presence of long‐range order in the system. Actually the formulation given is general enough as to render DODS as a special case. As shown, we may also obtain a ferrimagnetic as well as a density wave state solution depending on the special characteristics of the system at hand.A related type of antiferromagnetism is described by the Overhauser spin density wave (SDW) state and also this theory is formulated in a field theoretical language. The similarities and differences between DODS and SDW are discussed. The energy expressions for the two states are given within the Hartree‐Fock approximation.It is proposed that the SDW state could be used to partly account for the correlation problem in molecules, as well as the method of DODS which has previously been employed for that purpose.