Boson Subsidiary Solver (BoSS) v1.1

Abstract

How best to model systems of interacting electrons in an accurate and computationally efficient manner is an outstanding problem in theoretical and computational materials science. For materials where strong electronic interactions are primarily of a localized character and act within a subspace of localized quantum states on separate atomic sites (e.g., in transition metal and rare-earth compounds), their electronic behaviors are typically described by the Hubbard model and its extensions. In this work, we describe BoSS (Boson Subsidiary Solver), a software implementation of the subsidiary-boson (also known as slave-boson or auxiliary-boson) method appropriate for describing a variety of extended Hubbard models, namely p−d models that include both the interacting atomic sites (“d” states) and non-interacting or ligand sites (“p” states). We provide a theoretical background, a description of the equations solved by BoSS, an overview of the algorithms used, the key input/output and control variables of the software program, and tutorial examples of its use featuring band renormalization in SrVO3, Ni 3d multiplet structure in LaNiO3, and the relation between the formation of magnetic moments and insulating behavior in SmNiO3. BoSS interfaces directly with popular electronic structure codes: it can read the output of the Wannier90 software package [1,2] which postprocesses results from workhorse electronic structure software such as Quantum Espresso [3] or VASP [4]. Program summaryProgram title: Boson Subsidiary Solver (BoSS)CPC Library link to program files:https://doi.org/10.17632/3bwx6prn2w.1Developer's repository link:bitbucket.org/yalebosscode/bossCode Ocean capsule:https://codeocean.com/capsule/9605047Licensing provisions: Creative Commons by 4.0Programming language: MATLAB [5]Nature of problem: The BoSS approach, a type of subsidiary-boson method (also called slave-boson or auxiliary-boson method), provides approximate solutions to interacting electron problems described by Hubbard models in a computationally efficient manner. Hubbard models are widely used to describe materials systems with strongly localized electron-electron interactions. The interacting fermion problem is mapped onto two separate, but easier, coupled quantum problems: non-interacting fermions moving on a lattice (spinons) via tunneling between nearby atomic orbitals, and interacting subsidiary bosons that live on individual atomic sites. A self-consistent description of the two degrees of freedom requires matching of mean particle numbers (spinons and bosons) on each site as well as the renormalization of tunneling events for one set of particles due to the fluctuations of the other set of particles. The method can be used to describe the interacting electronic ground state of a particular electronic configuration, or more generally it can find the minimum energy electronic configuration by searching over various symmetry broken phases (e.g., magnetic configurations, configurations with unequal occupation of nominally equivalent atomic orbitals, etc.)Solution method: The spinon and subsidiary-boson problems are each represented as Hermitian eigenvalue problems where the lowest energy (eigenvalue) state is sought. The present implementation uses dense matrix digaonalization for the spinon problem and can use either dense or sparse matrix diagonalization for the boson problem. Particle number matching between the two descriptions is achieved by adjustment of Lagrange multipliers which represent potential energies for the bosons: their appropriate values are found by applying Newton's method to match spinon and boson occupancies. Self-consistency is achieved by simple fixed point iteration (solving spinon, then subsidiary, then spinon, etc.) Minimization of the energy uses gradient descent with adjustable step size.Additional comments including restrictions and unusual features: Most users will prepare the input data for BoSS by running band structure calculations on a material, e.g., density functional theory (DFT) using available software packages such as Quantum Espresso [3] or VASP [4]. Post processing of these calculations to create a spatially localized basis set provides the input to BoSS: most users will create the localized description by using software that transforms the electronic description into a Wannier function basis such as Wannier90 [1] which BoSS interfaces with by default. However, one can bypass this approach and create BoSS input files manually to describe specific localized electron models. Referenceshttp://bitbucket.org/yalebosscode/bosshttp://www.wannier.org/https://www.quantum-espresso.org/https://www.mathworks.com/products/matlab.htmlhttps://www.vasp.at/