Density profiles in random quantum spin chains

We consider random transverse-field Ising spin chains and study the magnetization and the energy-density profiles by numerically exact calculations in rather large finite systems (L less than or equal to 128). Using different boundary conditions (foe, fixed, and mixed) the numerical data collapse to scaling functions, which are very accurately described by simple analytic expressions. The average magnetization profiles satisfy the Fisher-de Gennes scaling conjecture and the corresponding scaling functions are indistinguishable from those predicted by conformal invariance.