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Slave Boson
The slave boson method is a technique for dealing with models of strongly correlated systems, providing a method to second-quantize valence fluctuations within a restrictive manifold of states. In the 1960s the physicist John Hubbard introduced an operator, now named the "Hubbard operator" to describe the creation of an electron within a restrictive manifold of valence configurations. Consider for example, a rare earth or actinide ion in which strong Coulomb interactions restrict the charge fluctuations to two valence states, such as the Ce4+(4f0) and Ce3+ (4f1) configurations of a mixed-valence cerium compound. The corresponding quantum states of these two states are the singlet \vert f^0\rangle state and the magnetic \vert f^1:\sigma\rangle state, where \sigma=\uparrow,\ \downarrow is the spin. The fermionic Hubbard operators that link these states are then The algebra of operators is closed by introducing the two bosonic operators Together, these operators satisfy the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strongly Correlated Material
Strongly correlated materials are a wide class of compounds that include insulators and electronic materials, and show unusual (often technologically useful) electronic and magnetic properties, such as metal-insulator transitions, heavy fermion behavior, half-metallicity, and spin-charge separation. The essential feature that defines these materials is that the behavior of their electrons or spinons cannot be described effectively in terms of non-interacting entities. Theoretical models of the electronic ( fermionic) structure of strongly correlated materials must include electronic ( fermionic) correlation to be accurate. As of recently, the label quantum materials is also used to refer to strongly correlated materials, among others. Transition metal oxides Many transition metal oxides belong to this class which may be subdivided according to their behavior, ''e.g.'' high-Tc, spintronic materials, multiferroics, Mott insulators, spin Peierls materials, heavy ferm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Hubbard (physicist)
John Hubbard ( – ) was a British physicist working in the areas of solid-state and condensed matter physics. He is best known for the Hubbard model for interacting electrons and the Hubbard-Stratonovich transformation, both of which have found many applications beyond his original work. Early life and education John Hubbard was born on to Charles and Marion Hubbard. He spent most of his childhood in Teddington, London, and lived with his parents through his university education. Hubbard attended Hampton Grammar School and then entered Imperial College London. He received his Bachelor of Science in 1955, and his PhD in 1958 under the supervision of Stanley Raimes in the Department of Mathematics. For his thesis he worked on the “dielectric approach” to treating the Coulomb interaction between electrons in metals. Immediately thereafter he was hired to work at the Atomic Energy Research Establishment, Harwell by Brian Flowers, who was at the time head of the Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cerium
Cerium is a chemical element; it has Chemical symbol, symbol Ce and atomic number 58. It is a hardness, soft, ductile, and silvery-white metal that tarnishes when exposed to air. Cerium is the second element in the lanthanide series, and while it often shows the oxidation state of +3 characteristic of the series, it also has a stable +4 state that does not oxidize water. It is considered one of the rare-earth elements. Cerium has no known biological role in humans but is not particularly toxic, except with intense or continued exposure. Despite always occurring in combination with the other rare-earth elements in minerals such as those of the monazite and bastnäsite groups, cerium is easy to extract from its ores, as it can be distinguished among the lanthanides by its unique ability to be oxidized to the +4 state in aqueous solution. It is the most common of the lanthanides, followed by neodymium, lanthanum, and praseodymium. Its estimated abundance of elements in Earth's crust, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identity. In other words, a Lie algebra is an algebra over a field for which the multiplication operation (called the Lie bracket) is alternating and satisfies the Jacobi identity. The Lie bracket of two vectors x and y is denoted ,y/math>. A Lie algebra is typically a non-associative algebra. However, every associative algebra gives rise to a Lie algebra, consisting of the same vector space with the commutator Lie bracket, ,y= xy - yx . Lie algebras are closely related to Lie groups, which are groups that are also smooth manifolds: every Lie group gives rise to a Lie algebra, which is the tangent space at the identity. (In this case, the Lie bracket measures the failure of commutativity for the Lie group.) Conversely, to any finite-di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wick's Theorem
Wick's theorem is a method of reducing high- order derivatives to a combinatorics problem. It is named after Italian physicist Gian Carlo Wick. It is used extensively in quantum field theory to reduce arbitrary products of creation and annihilation operators to sums of products of pairs of these operators. This allows for the use of Green's function methods, and consequently the use of Feynman diagrams in the field under study. A more general idea in probability theory is Isserlis' theorem. In perturbative quantum field theory, Wick's theorem is used to quickly rewrite each time ordered summand in the Dyson series as a sum of normal ordered terms. In the limit of asymptotically free ingoing and outgoing states, these terms correspond to Feynman diagrams. Definition of contraction For two operators \hat and \hat we define their contraction to be :\hat^\bullet\, \hat^\bullet \equiv \hat\,\hat\, - \mathopen \hat\,\hat \mathclose where \mathopen \hat \mathclose denotes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piers Coleman
Piers Coleman (born 1958) is a British-born theoretical physicist, working in the field of theoretical condensed matter physics. Coleman is professor of physics at Rutgers University in New Jersey and at Royal Holloway, University of London. Education and career Coleman was raised in Cheltenham, England, where he attended Cheltenham Grammar School, graduating in 1976. He completed his undergraduate education at Trinity College, Cambridge, pursuing the Natural Sciences Tripos and the Mathematics Tripos part III under the mentorship of Gilbert Lonzarich. In 1980 he won a Jane Eliza Procter Fellowship to Princeton University where he studied theoretical condensed matter physics with Philip Warren Anderson. Contemporaries in the Princeton graduate physics program included Gabriel Kotliar, Cumrun Vafa, Nathan Mhyrvold and Jennifer Chayes. He was awarded a Junior Research Fellowship at Trinity College, Cambridge, which he held from 1983 to 1988. He was a postdoctoral fello ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resonating Valence Bond Theory
In condensed matter physics, the resonating valence bond theory (RVB) is a theoretical model that attempts to describe high-temperature superconductivity, and in particular the superconductivity in cuprate compounds. It was proposed by P. W. Anderson and Ganapathy Baskaran in 1987. The theory states that in copper oxide lattices, electrons from neighboring copper atoms interact to form a valence bond, which locks them in place. However, with doping, these electrons can act as mobile Cooper pairs and are able to superconduct. Anderson observed in his 1987 paper that the origins of superconductivity in doped cuprates was in the Mott insulator nature of crystalline copper oxide. RVB builds on the Hubbard and t-J models used in the study of strongly correlated materials. In 2014, evidence showing that fractional particles can happen in quasi two-dimensional magnetic materials, was found by EPFL scientists, lending support for Anderson's theory. Description The physics of Mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heavy Fermion
In materials science, heavy fermion materials are a specific type of intermetallic compound, containing elements with 4f or 5f electrons in unfilled electron bands. Electrons are one type of fermion, and when they are found in such materials, they are sometimes referred to as heavy electrons. Heavy fermion materials have a low-temperature specific heat whose linear term is up to 1000 times larger than the value expected from the free electron model. The properties of the heavy fermion compounds often derive from the partly filled f-orbitals of rare-earth or actinide ions, which behave like localized magnetic moments. The name "heavy fermion" comes from the fact that the fermion behaves as if it has an effective mass greater than its rest mass. In the case of electrons, below a characteristic temperature (typically 10 K), the conduction electrons in these metallic compounds behave as if they had an effective mass up to 1000 times the free particle mass. This large effecti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
