Applications Of Density Functional Theory In Computational Condensed Matter Physics And Development Of Linear Scaling Method

With the rapid development of computer science and numerical methods,computational physics has solved many physical problems that traditional methods could not solve in the past few decades.Its value has been widely recognized and has become an equally important branch of physics along with theoretical physics and experimental physics.Computational condensed matter physics is a discipline that studies condensed matter systems from the perspective of computational physics.As the name suggests,condensed matter systems are quantum systems composed of a large number of interacting atoms and molecules.In general,the physical properties of the system can be determined by solving the Schr?dinger equation.However,due to the high computational complexity,it is often impossible to accurately solve the Schr?dinger equation of condensed matter systems,and even approximate solutions are difficult to achieve.Therefore,finding effective many-body methods has become the key issue of computational condensed matter physics.In the past hundred years,a series of many-body computational methods such as exact diagonalization method,density functional theory,quantum Monte Carlo method,renormalization group theory,and dynamic mean field theory have emerged.These methods provide practical and effective tools for condensed matter physics and have profoundly influenced the development of condensed matter physics today.Among them,density functional theory,as an important breakthrough in computational condensed matter physics,has opened the door to first-principles quantitative calculations of actual materials.Kohn-Sham density functional theory,which combines accuracy and efficiency,is one of the most successful many-body numerical calculation methods today and is widely used in fields such as molecular physics,chemistry,and materials science.Kohn-Sham density functional theory gives the single-electron eigen-wavefunctions and eigenenergies of the system’s ground state.Combined with other physical theories such as linear response theory and Boltzmann transport theory etc,it can calculate various physical properties of condensed matter systems.With the development of computer science,since the end of the last century,a large number of computational software packages based on density functional theory have emerged.These software packages greatly reduce the difficulty in simulating condensed matter systems and have made great contributions to related research fields.The first two works of this thesis will apply density functional theory to study real condensed matter systems and conduct theoretical research on some valuable and unresolved physical problems through first-principles calculations.Chapter 3 will introduce the theoretical research on finding low-dimensional half-metal using density functional theory calculations.Chapter 4 will introduce the applications of density functional theory calculations to study the optical properties of topological nodal-line semimetal Zr Si S and the modulation effect of uniaxial stress.In addition,the implementation of Kohn-Sham density functional theory generally requires diagonalization or orthogonalization of the Hamiltonian to obtain single-electron wave functions.The time consumption increases with the cube of the system size,and the memory consumption increases with the square of the system size.Therefore,the application of density functional theory is severely limited by the size of the system.In general,even on an advanced cluster,density functional theory is difficult to handle systems with thousands of atoms.To this day,some systems that are at the forefront of condensed matter physics research,such as twisted graphene,fractals,and quasicrystals,have no periodicity or very large periodicity.These large-scale systems can hardly be simulated under the first-principles accuracy of density functional theory and can only be studied using empirical models such as tight-binding models and continuous models.How to avoid matrix diagonalization and develop a low-scale density functional theory algorithm while retaining the high accuracy of Kohn-Sham density functional theory has become the key to expanding its application scale.In order to solve the application limitation of density functional theory in large-scale systems,Chapter 5 will introduce how the author innovatively proposed to use random state time evolution instead of diagonalization to solve the Kohn-Sham Schr?dinger equation under the guidance of his tutor after many years of attempts and research.The diagonalization-free calculation from Hamiltonian to electron density is realized and a new sublinear-scale density functional theory calculation method rs DFT is developed based on this.In general,this thesis has carried out a series of researches around the computational method of density functional theory and has achieved results in both practical system applications and numerical algorithm development.The specific summary is as follows:(1)Edge magnetism and tunable half-metallic properties of one-dimensional edgehydrogenated indium selenide nanoribbons.half-metals are widely used in spintronic devices,and finding structurally stable and easily tunable low-dimensional half-metals is a key issue in spintronics.Through density functional theory calculations,this thesis finds that edge-hydrogenated indium selenide nanoribbons have localized magnetic moments localized along the zigzag edges.In hybrid functional calculations,the energy gap of one spin is significantly enlarged,so that half-metallic property that can be realized by doping within a certain energy range near the Fermi surface.Based on the results of first-principles theoretical calculations,we fitted a two-band tight-binding model using local Wannier functions and mapped it into the Heisenberg model.Using the Heisenberg model,we systematically studied the magnetic exchange interaction strength of the edge magnetic moments of the nanoribbon,the zero-temperature magnetic ground state,and thermal stability at finite temperatures.Finally,through the calculation of conductivity,it is pointed out that spin current can be induced in the nanoribbon by p-type charge doping.(2)Broad-spectrum optical properties of topological nodal line semimetal Zr Si S and modulation effect of uniaxial stress on it.Recent optical measurements on topological nodal line semimetal Zr Si S have found novel optical responses in the infrared region,and transport experiments also indicate that it may undergo topological phase transitions under uniaxial stress.In order to deeply and comprehensively understand the optical properties and stress effects of Zr Si S,it is urgent to carry out research on its broad-spectrum optical response and examine the modulation effect of uniaxial stress.This thesis uses density functional theory calculations combined with linear response theory to point out that the constant optical conductivity observed in experiments in the low-ener gy region is closely related to band-to-band transitions,and further points out that there is a widely applicable low-loss hyperbolic plasmon excitation in the deep ultraviolet region at 20 e V.After applying uniaxial stress,the electronic structure at the Fermi surface of Zr Si S will undergo two Lifshitz phase transition under certain pressure,and the corresponding optical properties in the low-energy region will also change.In addition,the ultraviolet plasmon dispersion can be effectively modulated by uniaxial stress.The theoretical predictions of Lifshitz phase transitions and other optical changes under stress in this study have been confirmed by recent experimental articles.(3)Developed a sublinear-scale algorithm rs DFT within the framework of KohnSham density functional theory.This thesis proposes a new method based on random state time evolution methods to solve electron density based on Kohn-Sham equations to achieve self-consistent field calculations.This method bypasses diagonalization operations in traditional density functional theory calculations,transforms the problem of solving stationary Schr?dinger equations into solving time-dependent Schr?dinger equations,calculates global physical quantities(such as density of states,Fermi energy,total energy)and local physical quantities(such as spatial distribution of electron density)through time evolution of random wave functions.The accuracy of new method is automatically improved as system size or number of random states increases.Specifically,when the system approaches thermodynamic limit,all physical quantities can be accurately calculated with only one random state time evolution.This brand-new density functional theory algorithm has sublinear scaling characteristics overall and provides new possibilities for first-principles calculation simulations of large-scale condensed matter systems.