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 summary

Program title: Boson Subsidiary Solver (BoSS)

CPC Library link to program files: https://doi.org/10.17632/3bwx6prn2w.1

Developer's repository link: bitbucket.org/yalebosscode/boss

Code Ocean capsule: https://codeocean.com/capsule/9605047

Licensing provisions: Creative Commons by 4.0

Programming 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.

References

http://bitbucket.org/yalebosscode/boss

http://www.wannier.org/

https://www.quantum-espresso.org/

https://www.mathworks.com/products/matlab.html

https://www.vasp.at/

中文翻译：

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Boson子公司求解器（BoSS）v1.1

在理论和计算材料科学中，如何最好地准确地以准确且计算高效的方式对相互作用的电子系统建模是一个突出的问题。对于那些强烈的电子相互作用主要具有局部性并且在单独的原子位点（例如，在过渡金属和稀土化合物中）的局部量子态的子空间中起作用的材料，其电子行为通常由Hubbard模型及其特征来描述。扩展名。在本文中，我们描述BoSS（玻色子子求解器），它是子玻色子（也称为从玻色子或辅助玻色子）方法的软件实现，适用于描述各种扩展的Hubbard模型，即$p-d$同时包含相互作用原子位点（“ d ”状态）和非相互作用或配体位点（“ p ”状态）的模型。我们提供了理论背景，对BoSS解决的方程式的描述，所用算法的概述，软件程序的关键输入/输出和控制变量，以及在SrVO ₃，Ni 3中具有能带重归一化的用法示例教程LaNiO _3中的d多重结构以及SmNiO ₃中磁矩的形成与绝缘行为之间的关系。BoSS直接与流行的电子结构代码进行接口：它可以读取Wannier90软件包[1]，[2]的输出，该软件包对诸如Quantum Espresso [3]或VASP [4]等主力电子结构软件的结果进行后处理。

计划摘要

计划名称：Boson Subsidiary Solver（BoSS）

CPC库链接到程序文件： https : //doi.org/10.17632/3bwx6prn2w.1

开发人员的资料库链接： bitbucket.org/yalebosscode/boss

代码海洋胶囊： https : //codeocean.com/capsule/9605047

许可条款： Creative Commons by 4.0

编程语言： MATLAB [5]

问题性质：BoSS方法是一种辅助玻色子方法（也称为从玻色子或辅助玻色子方法），它以有效的计算方式为由Hubbard模型描述的相互作用的电子问题提供了近似的解决方案。哈伯德模型被广泛用于描述具有强烈局部电子-电子相互作用的材料系统。相互作用的费米子问题被映射到两个单独的但更容易耦合的量子问题上：通过附近原子轨道之间的隧穿在晶格（自旋子）上移动的非相互作用费米子，以及生活在各个原子位点上的相互作用的子玻色子。对两个自由度的自洽描述需要在每个位置上匹配平均粒子数（自旋子和玻色子），以及由于另一组粒子的波动而使一组粒子的隧穿事件重新归一化。该方法可用于描述特定电子配置的相互作用电子基态，或更普遍地说，它可以通过搜索各种对称的断相（例如，磁性配置，名义上等效原子的占有不相等的配置）来找到最小能量的电子配置。轨道等）

求解方法：旋子和子玻色子问题分别表示为寻求最低能量（特征值）状态的埃尔米特特征值问题。本实施方式将稠密的矩阵对角化用于棘手问题，并且可以将稠密的或稀疏的矩阵对角化用于玻色子问题。两种描述之间的粒子数匹配是通过调整表示玻色子势能的拉格朗日乘数来实现的：通过应用牛顿方法来匹配旋子和玻色子的占有率，可以找到它们的适当值。通过简单的定点迭代（求解尖峰，然后是子级，然后是尖峰，等等）来实现自洽。最小化能量使用具有可调步长的梯度下降。

其他注释包括限制和异常功能：大多数用户将通过使用诸如Quantum Espresso [3]或VASP [4]等可用软件包在材料上进行带结构计算，例如密度泛函理论（DFT），为BoSS准备输入数据。。这些计算的后处理以创建空间局部化的基础集，从而为BoSS提供输入：大多数用户将通过使用将电子描述转换为Wannier函数基础的软件（例如Wannier90 [1]）来创建局部化的描述，该软件默认与BoSS进行接口。但是，人们可以绕过这种方法并手动创建BoSS输入文件来描述特定的局部电子模型。

参考

http://bitbucket.org/yalebosscode/boss

http://www.wannier.org/

https://www.quantum-espresso.org/

https://www.mathworks.com/products/matlab.html

https://www.vasp.at/