Nonadiabatic extension of the Heisenberg model

Abstract

The localized states within the Heisenberg model of magnetism should be represented by best localized Wannier functions forming a unitary transformation of the Bloch functions of the narrowest partly filled energy bands in the metals. However, as a consequence of degeneracies between the energy bands near the Fermi level, in any metal these Wannier functions cannot be chosen symmetry-adapted to the complete paramagnetic group M P . Therefore, it is proposed to use Wannier functions with the reduced symmetry of a magnetic subgroup M of M P [case (a)] or spin dependent Wannier functions [case (b)]. The original Heisenberg model is reinterpreted in order to understand the pronounced symmetry of these Wannier functions. While the original model assumes that there is exactly one electron at each atom, the extended model postulates that in narrow bands there are as many as possible atoms occupied by exactly one electron. However, this state with the highest possible atomiclike character cannot be described within the adiabatic (or Born-Oppenheimer) approximation because it requires a more realistic description of the electronic motion. Within the (true) nonadiabatic system the electrons move on localized orbitals that are still symmetric on the average of time, but not at any moment. These nonadiabatic states have the same symmetry as the adiabatic states and determine the commutation properties of the nonadiabatic Hamiltonian H n . The nonadiabatic Heisenberg model is a purely group-theoretical model which interprets the commutation properties of H n that are explicitly given in this paper for the two important cases (a) and (b). There is evidence that the occurrence of these two types of Wannier functions in the band structure of a metal is connected with the occurrence of magnetism and superconductivity, respectively.

Antiferromagnetic, neutral, and superconducting band in La2CuO4

“…Observations on the band structures of Fe [4] and Cr [5] suggest that in both Fe and Cr a narrow, roughly half-filled magnetic band is responsible for the stability of the ferromagnetic and the (antiferromagnetic) spin-density wave state, respectively, in these materials. This observation can be interpreted within a nonadiabatic extension of the Heisenberg model, the "nonadiabatic Heisenberg model" (NHM) [6].…”

“…(A21) and (A22) in Ref. [6]. Also energy bands with optimally localizable and symmetry-adapted spindependent Wannier functions situated at the Cu atoms follow Eq.…”

“…(2.20) and (5.3) of Ref. [6] for the superconducting and magnetic state, respectively, and may be assumed to be independent of the Sr concentration x since the physically relevant copper-oxygen planes are not seriously affected by the doping.…”

“…All the Wannier functions considered in this paper are centered at the Cu atoms because La 2 CuO 4 has a single conduction band [6].…”

k-Space Magnetism as the Origin of Superconductivity

“…The nonadiabatic Heisenberg model (NHM) [1] is an extension of the Heisenberg model [2] going beyond the adiabatic approximation. It is based on three postulates related to the atomic-like motion [2][3][4] of the electrons in narrow, roughly half-filled energy bands.…”