T = 0 finite-size scaling for a quantum system with long-range interaction

The general idea of finite size scaling are tested by the example of the pure quantum version of an exactly solvable model of structural phase transition with long-range interaction decaying at large distances r as r-d-σ, where d is the space dimensionality and σ > 0. The finite size shift of the quantum parameter (playing the same role as that of the temperature for classical systems) is calculated for the general geometry Ld−d′ × ∞d′, with 0 < d′ < d. The root mean square order parameter is evaluated for 0 < d′ < σ/2.