Symmetry breaking,quantum protectorate and quasiaverages in condensed matter physics

Substantial progress in the understanding of the spontaneously broken symmetry concept is connected with Bogoliubov’s fundamental ideas about quasiaverages. The development and applications of the method of quasiaverages, formulated by N. N. Bogoliubov, to quantum statistical mechanics and to quantum solid state theory and, in particular, to quantum theory of magnetism, are discussed. Some physical implications involved in a new concept, termed the quantum protectorate, are considered.     

Broken spin symmetry approach to chemical reactivity and magnetism of graphenium species

The basic problem of weak interaction between odd electrons in graphene and silicene is considered in the framework of the broken spin symmetry approach. This approach exhibits the peculiarities of the odd-electron behavior via both enhanced chemical reactivity and magnetism.     

Distorted magnetic orders and electronic structures for FeSe under pressure

We have studied various magnetic orders and electronic properties as well as pressure-induced effects on FeSe by using density functional theory with combination of Hubbard Model. We find that the Fe spins in striped antiferromagnetic orders with the broken symmetry are more stable in energy than the checkerboard antiferromagnetic ones with tetragonal symmetry. The electronic properties revealed that the enhanced metallic and the suppressed magnetism caused by quantum many-body effects would be the origin for the occurrence of pressure-induced superconductivity in FeSe system, which indicate that the superconductivity of FeSe system showed a closed relationship with the magnetism and its spin fluctuation. These results are useful in understanding the structural, magnetic and electronic properties of FeSe under pressure.     

Lectures on renormalization and asymptotic safety

A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ$\sigma$ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method.     

Magnetic properties of quantum dots and rings

Exact many-body methods as well as current-spin-density functional theory are used to study the magnetism and electron localization in two-dimensional quantum dots and quasi-one-dimensional quantum rings. Predictions of broken-symmetry solutions within the density functional model are confirmed by exact configuration interaction (CI) calculations: In a quantum ring the electrons localize to form an antiferromagnetic chain which can be described with a simple model Hamiltonian. In a quantum dot the magnetic field localizes the electrons as predicted with the density functional approach. Received 5 December 2000     

$\mathcal{PT}$ Symmetry in Statistical Mechanics and the Sign Problem

Generalized PT\mathcal{PT} symmetry provides crucial insight into the sign problem for two classes of models. In the case of quantum statistical models at non-zero chemical potential, the free energy density is directly related to the ground state energy of a non-Hermitian, but generalized PT\mathcal{PT}-symmetric Hamiltonian. There is a corresponding class of PT\mathcal{PT}-symmetric classical statistical mechanics models with non-Hermitian transfer matrices. We discuss a class of Z(N) spin models with explicit PT\mathcal{PT} symmetry and also the ANNNI model, which has a hidden PT\mathcal{PT} symmetry. For both quantum and classical models, the class of models with generalized PT\mathcal{PT} symmetry is precisely the class where the complex weight problem can be reduced to real weights, i.e., a sign problem. The spatial two-point functions of such models can exhibit three different behaviors: exponential decay, oscillatory decay, and periodic behavior. The latter two regions are associated with PT\mathcal{PT} symmetry breaking, where a Hamiltonian or transfer matrix has complex conjugate pairs of eigenvalues. The transition to a spatially modulated phase is associated with PT\mathcal{PT} symmetry breaking of the ground state, and is generically a first-order transition. In the region where PT\mathcal{PT} symmetry is unbroken, the sign problem can always be solved in principle using the equivalence to a Hermitian theory in this region. The ANNNI model provides an example of a model with PT\mathcal{PT} symmetry which can be simulated for all parameter values, including cases where PT\mathcal{PT} symmetry is broken.     

Computational quantum magnetism: Role of noncollinear magnetism

We are witnessing today a golden age of innovation with novel magnetic materials and with discoveries important for both basic science and device applications. Computation and simulation have played a key role in the dramatic advances of the past and those we are witnessing today. A goal-driving computational science—simulations of every-increasing complexity of more and more realistic models has been brought into greater focus with greater computing power to run sophisticated and powerful software codes like our highly precise full-potential linearized augmented plane wave (FLAPW) method. Indeed, significant progress has been achieved from advanced first-principles FLAPW calculations for the predictions of surface/interface magnetism. One recently resolved challenging issue is the role of noncollinear magnetism (NCM) that arises not only through the SOC, but also from the breaking of symmetry at surfaces and interfaces. For this, we will further review some specific advances we are witnessing today, including complex magnetic phenomena from noncollinear magnetism with no shape approximation for the magnetization (perpendicular MCA in transition-metal overlayers and superlattices; unidirectional anisotropy and exchange bias in FM and AFM bilayers; constricted domain walls important in quantum spin interfaces; and curling magnetic nano-scale dots as new candidates for non-volatile memory applications) and most recently providing new predictions and understanding of magnetism in novel materials such as magnetic semiconductors and multi-ferroic systems.     

磁性外尔半金属材料研究现状与展望

外尔半金属是拓扑半金属家族中的一员。理想的外尔半金属费米面附近有且仅有非简并价带和导带形成的孤立能带交叉点,其低能激发准粒子可以用描述手性外尔费米子的外尔方程来刻画。在三维固体中形成外尔半金属态需要破缺时间反演、中心反演以及它们的组合对称操作。外尔点(即能带交叉点)具有拓扑稳定性和确定的手性或磁荷,且左右手性外尔点需成对出现。非磁性外尔半金属TaAs家族材料的发现,使得研究具有手征性的电子态,及其导致的新物性、新现象成为可能。与非磁性外尔半金属相比,磁性外尔半金属可以仅仅具有一对外尔点,是最简单的外尔半金属,有利于物理机理的分析。磁性外尔半金属可用于实现具有本征磁性的量子反常霍尔效应,提供了通过外磁场来调控外尔点及其相关效应的新手段。文章介绍了磁性外尔半金属的理论模型、拓扑数计算等基本原理,简要回顾了一些典型材料的理论计算和实验研究进展,并介绍了磁性拓扑量子化学理论和磁性拓扑材料的高通量计算,最后讨论了磁性外尔半金属的发展前景和未来的研究方向。     

Generic mixed columnar-plaquette phases in Rokhsar-Kivelson models

We revisit the phase diagram of Rokhsar-Kivelson models, which are used in fields such as superconductivity, frustrated magnetism, cold bosons, and the physics of Josephson junction arrays. From an extended height effective theory, we show that one of two simple generic phase diagrams contains a mixed phase that interpolates continuously between columnar and plaquette states. For the square lattice quantum dimer model we present evidence from exact diagonalization and Green's function Monte Carlo techniques that this scenario is realized, by combining an analysis of the excitation gaps of different symmetry sectors with information on plaquette structure factors. This presents a natural framework for resolving the disagreement between previous studies.     

Being Discrete about Yang and Mills: Basic Techniques of Euclidean Lattice Gauge Theory

We discuss the formulation of gauge-invariant quantum field theories (without dynamical matter fields) as statistical mechanics systems on four-dimensional Euclidean lattices. Approximation methods including strong- and weak-coupling expansions, mean-field theory and Monte Carlo simulations are reviewed in detail, and Abelian duality transformations are derived. New models are discussed. An action is defined on 2 × 1 rectangular loops of links and its properties are investigated. It is found to result in phase transitions in 2, 3 and 4 dimensions with Z(2) and SU(2) gauge groups. A large class of models with Z(N) symmetry realised on plaquettes is investigated, and several phase diagrams are presented. A mixed model with interactions through both plaquettes and rectangles is found to have a line of phase transitions and a critical point associated with the crossover region in the Wilson SU(2) model.     

Magnetic and electronic properties of Mn2Sn thin films: First-principles calculations and high temperature series expansions

In this paper, first-principles calculations have been performed in order to study the electronic and magnetic properties of the bulk and the (0 0 1) surface of Mn₂Sn thin films using self-consistent ab initio calculations, based on the density functional theory approach and using the product of the muffin-tin radius and the maximum reciprocal space vector, R_MT. K_max, we full potential linear augmented plane wave methods. Spin-polarized calculations within the framework of density-functional theory are a powerful tool for describing the magnetism of itinerant electrons in solid state materials. The total and partial density of states of Mn₂Sn thin films were calculated. The magnetic moments considered to lie along the c axes are computed. The data obtained from the ab initio calculations are used as an input for the high temperature series expansions calculations used to compute other magnetic parameters. The critical temperature and exchange interactions between the magnetic atoms in the Mn₂Sn thin films are obtained using high temperature series expansions and mean field theory, respectively.     

Crystal growth and dislocations

The article attempts to review the present stage of the density functional theory for noncollinear magnetic states and its application to particular physical problems. The discussion starts with basic theorems of the theory and derivation of the Kohn-Sham equation for a noncollinear magnet. Special features of solving this equation are illustrated using the augmented-spherical-wave method generalized to the noncollinear magnetic structures as an example. Particular attention is devoted to the symmetry of the problem. It is shown that a traditional approach of the space group theory fails in the case of a noncollinear magnetic state. A generalized approach based on the notion of the spin space groups is presented which allows a consequent treatment of the symmetry properties of both nonrelativistic and relativistic problems. This approach allows the development of an exact procedure for a first-principles calculation of an incommensurate spiral structure and gives a sound basis for the calculation and physical interpretation of the noncollinear magnetic structures caused by the effects of relativity. Application of the theory to the first-principles determination of the complex noncollinear magnetic structures of various systems are discussed. Applications include the spiral structure of fcc Fe, the uncompensated magnetic structure in U3X4 and compensated magnetic structure in U2P2Sn, and two different types of weak ferromagnetism in Fe2O3 and Mn3Sn. It is shown how the calculation technique can be applied to studies of unenhanced and enhanced non-uniform magnetic susceptibilities as well as susceptibilities in fields noncollinear to the atomic moments. Illustrating results of the calculation of the susceptibility of various systems are presented. The last part of the review is devoted to applications of the theory of noncollinear magnetism to studies of temperature effects in the electronic properties of itinerant magnets.     

Studying adequacy, completeness, and accuracy of quantum measurement protocols

A new methodology of statistical estimation of the quality of quantum measurement protocols is considered. The method is based on studying the completeness, adequacy, and accuracy of quantum measurement protocols. The completeness is estimated on the basis of considering a singular decomposition of a special matrix, which is constructed based on the measurement operators. The estimate of adequacy supposes the presence of redundancy in the measurement protocol as compared to the minimally possible number of measurements that are necessary for full reconstruction of a quantum state. The adequacy of quantum measurements is estimated as the degree of how much the redundant statistical data agree with the laws of quantum theory. The accuracy characteristics of the statistical reconstruction of arbitrary quantum states are studied based on the universal statistical distribution for accuracy losses. Examples of applying the developed methods are presented for seven quantum protocols based on the geometry of polyhedra with a high degree of symmetry.     

M-theory: Strings,duality and branes

String theory is an attempt to combine all of the known physical forces into a single unified framework. A powerful new type of duality symmetry has recently been discovered in string theory which has led to important breakthroughs. What were previously considered to be five distinct string theories are now known to be different aspects of an underlying structure called M-theory. In addition to strings, extended objects of higher dimension or 'branes', play a key role. We review these developments and discuss the impact that they are having on quantum field theory and the quantum properties of black holes.     

Statistical Gauge Theory for Relativistic Finite Density Problems

A relativistic quantum field theory is presented for finite density problems based on the principle of locality.It is shown that,in addition to the conventional ones,a local approach to the relativistic quantum field theories at both zero and finite densities consistent with the violation of Bell-like inequalities should contain and provide solutions to at least three additional problems,namely,i) the statistical gauge invariance;ii) the dark components of the local observables;and iii)the fermion statistical blocking effects,based upon an asymptotic nonthermal ensemble,An application to models is presented to show the importance of the discussions.     

Spontaneous symmetry breaking in quantum many-body systems (A solid-state physicist’s view of Goldstone’s theorem and all that)

The concept of spontaneous symmetry breaking arose first in the context of superconductivity, before it became important for elementary particle physics. Starting with its original discovery, a comparison of the workings of the Goldstone mechanism in relativistic quantum fixed theory on the one hand and in quantum statistical mechanics on the other is given. The roles of locality and of long range forces are traced. For condensed matter physics, an approach using functional integral methods and macroscopic order parameter fields, valid near critical points is outlined. A possibly more widely valid approach is also presented, to complete this review of the Goldstone theories in quantum statistical mechanics. Talk delivered at the International Symposium on Theoretical Physics, Bangalore, November 1984.     

Dynamical mass generation in BRS invariant theories

The problem of the origin of the gauge particle's mass is considered in the framework of the BRS symmetry. A new approach is suggested where the global gauge group symmetry of the quantum theory is hidden by the condensation of bound states of the ghost fields in the perturbative vacuum. Dynamical mass generation for the gauge fields follows the Schwinger mechanism.     

Vortices in Landau-Ginzburg theories of anyonic superconductivity

We study in detail the structure and properties of vortices in a recently proposed effective Landau-Ginzburg theory of anyonic superconductivity. The theory is described by a Chern-Simons gauge theory interacting with a complex scalar field in a broken symmetry phase. We analyze the profiles for the magnetic field, charge density, electric fie]d and angular momentum in a wide range of parameters between the Abrikosov-Nielsen-Olesen and pure Chern-Simons limits. For small values of the statistical parameter the magnetic field nucleates near the normal core, but is localized away from the core and well into the superconducting region in the Chern-Simons limit. In all cases, the charge density, electric field and magnetic moment density are localized within a ring surrounding the normal core. The unusual properties and quantum numbers of these vortices are studied.