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Springer eBooks

Correlated basis function theory for fermion systems

Stefano Fantoni, Adelchi Fabrocini

Published Apr 7, 2008• 16 citations
Publisher
DOI
10.1007/bfb0104526

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Abstract This paper presents the derivation of a kinetic-balance condition for explicitly correlated basis functions employed in semi-classical relativistic calculations. Such a condition is important to ensure variational stability in algorithms based on the first-quantized Dirac theory of 1/2-fermions. We demonstrate that the kinetic-balance condition can be obtained from the row reduction process commonly applied to solve systems of linear equations. The resulting form of kinetic balance establishes a relation for the components of the spinor of an N -fermion system to the non-relativistic limit, which is in accordance with recent developments in the field of exact decoupling in relativistic orbital-based many-electron theory.
We consider the XXZ spin chain in the scaling limit in the Matsubara direction. The main result of this paper is new representations for the functions Ψ(l,κ)\Psi(l, \kappa)Ψ(l,κ) and Θ(l,m;κ,α)\Theta(l, m; \kappa, \alpha)Θ(l,m;κ,α) associated with the function ω(ζ,ξ;κ,κ)\omega(\zeta, \xi; \kappa, \kappa)ω(ζ,ξ;κ,κ) found in the expression for the correlation function of the generators of the fermionic basis for the XXZ spin chain. The final result incorporates the case of particle-hole excitations which is needed for the relation of the fermionic basis to the Virasoro basis of the CFT descendants.