Renormalization spin waves

The elementary excitations of the system are thus non-interacting renormalized spin waves with energies E T) determined by the diagonalization of as... 

Rommer, S., Ostlund, S. Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group. Phys. Rev. B 1997, 55(4), 2164. 

This output displays part of the information that is given by the XMVB program at the end of an L-VBCISD calculation on F2. Each fundamental structure is a linear combination of VB functions that possess the same nature in terms of spin-pairing and charge distributions. The coefficients of these VB functions are extracted from the multistructure ground-state wave function, and are renormalized (see Eqs. 9.13-9.14). 

Renormalization factors grijUt) calculated for A 208 nuclei with HO wave functions ha> = 6.88 MeV) and both the H7B and HBB residual interactions. Results are for the ten possible RO transitions in the model space of Fig. 2. For HO wave functions the qs are given by 1 — gj = qj- — 1. A breakdown into the tensor and central contributions is given. The columns labeled central also contain a small spin-orbit contribution. Note the similarity of the central contributions for the H7B and HBB interactions and that the H7B tensor component is larger than that of the HBB interaction... 

A popular method of removing unwanted states is to project them out with a suitable projection operator (in the picture of the wave function being described in the coordinate system consisting of determinants, the components of the wave function along the higher spin states is removed). As mentioned above, the next higher spin state is usually the most important, and in many cases it is a quite good approximation to only remove this state. After projection, the wave function is then renormalized. If only the first contaminant is removed, this may in extreme cases actually increase the (S ) value. 

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