Density-functional formulations for quantum chains

TL;DR

This paper develops a lattice density-functional theory for quantum spin chains, enabling predictions of various physical properties and exploring local and nonlocal approximations for improved accuracy.

Contribution

It introduces a DFT formalism for quantum spin chains, applying renormalization-group concepts and comparing local and nonlocal approximations for critical phenomena.

Findings

Nonlocal functionals outperform LDA in predictions.

DFT formalism successfully predicts energy gaps and critical exponents.

Local-density approximation has limited accuracy for critical properties.

Abstract

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 {\em 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; (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.