Density-functional formulations for quantum chains

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.

7 figures, 5 tables

References in corpus (13)

• Friedel Oscillations and Charge Density Waves in Chains and Ladders
• Density-functionals not based on the electron gas: Local-density approximation for a Luttinger liquid
• Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices
• What can Mott insulators teach us about density-functional theory (and vice versa)?
• Friedel Oscillations in the Open Hubbard Chain
• Exact Solution of the Asymmetric Exclusion Model with Particles of Arbitrary Size
• Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas
• Phase Coherence in a Random One-Dimensional System of Interacting Fermions: A Density Matrix Renormalization Group Study
• Phase diagram of harmonically confined one-dimensional fermions with attractive and repulsive interactions
• Effects of nanoscale spatial inhomogeneity in strongly correlated systems
• Spin-distribution functionals and correlation energy of the Heisenberg model
• Spin-density-functional theory: some open problems and application to inhomogeneous Heisenberg models
• Impurity and boundary effects in one and two-dimensional inhomogeneous Heisenberg antiferromagnets

Cited by in corpus (6)

• The Hubbard Dimer: A density functional case study of a many-body problem
• Machine learning density functional theory for the Hubbard model
• Successes and failures of Bethe Ansatz Density Functional Theory
• Current Density Functional Theory for one-dimensional fermions
• Extensibility of Hohenberg-Kohn Theorem to general quantum systems
• Testing density functional theory in a quantum Ising chain