We show that a lattice formulation of density functional theory (DFT), guided by renormalization-group concepts, can be used to obtain numerical predictions of energy gaps, spin-density profiles, critical exponents, sound velocities, surface energies, and conformal anomalies of spatially inhomogeneous quantum-spin chains. To this end, we (i) cast the formalism of DFT in the notation of quantum-spin chains to make the powerful methods and concepts developed in ab initio DFT available to workers in this field, (ii) explore to what extent simple local approximations in the spirit of the local-density approximation (LDA) can be used to predict critical exponents and conformal anomalies of quantum-spin models, and (iii) propose and explore various nonlocal approximations depending on the size of the system or on its average density in addition to the local density. These nonlocal functionals turn out to be superior to LDA functionals.

• Received 5 February 2007

DOI:https://doi.org/10.1103/PhysRevB.76.035109