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Dynamical Mean-field Theory
Dynamical mean-field theory (DMFT) is a method to determine the electronic structure of strongly correlated materials. In such materials, the approximation of independent electrons, which is used in density functional theory and usual band structure calculations, breaks down. Dynamical mean-field theory, a non-perturbative treatment of local interactions between electrons, bridges the gap between the nearly free electron gas limit and the atomic limit of condensed-matter physics. DMFT consists in mapping a many-body lattice problem to a many-body ''local'' problem, called an impurity model. While the lattice problem is in general intractable, the impurity model is usually solvable through various schemes. The mapping in itself does not constitute an approximation. The only approximation made in ordinary DMFT schemes is to assume the lattice self-energy to be a momentum-independent (local) quantity. This approximation becomes exact in the limit of lattices with an infinite coordina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strongly Correlated Materials
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) electronic correlation, 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-temperature superconductivity, high-Tc, spintronics, spintronic materials, multiferro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ising Model
The Ising model (or Lenz–Ising model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical models in physics, mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent Nuclear magnetic moment, magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a Graph (abstract data type), graph, usually a lattice (group), lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors. Neighboring spins that agree have a lower energy than those that disagree; the system tends to the lowest energy but heat disturbs this tendency, thus creating the possibility of different structural phases.The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition. Though it is a highly simplified model of a magnetic material, the Ising model can sti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Function
''Spectral'' is a 2016 Hungarian-American military science fiction action film co-written and directed by Nic Mathieu. Written with Ian Fried & George Nolfi, the film stars James Badge Dale as DARPA research scientist Mark Clyne, with Max Martini, Emily Mortimer, Clayne Crawford, and Bruce Greenwood in supporting roles. The film is set in a civil war-ridden Moldova as invisible entities slaughter any living being caught in their path. The film was released worldwide on December 9, 2016 on Netflix. On February 1, 2017, Netflix released a prequel graphic novel of the film called ''Spectral: Ghosts of War'' which was made available digitally through the website ComiXology. Plot DARPA researcher Mark Clyne is sent to a US military airbase on the outskirts of Chișinău, to consult his created line of hyperspectral imaging goggles issued to US Army Special Forces led by Army General James Orland, who is covertly supporting the Moldovan government in an ongoing civil war against ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Exponents
Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems at thermal equilibrium, the critical exponents depend only on: * the dimension of the system * the range of the interaction * the spin dimension These properties of critical exponents are supported by experimental data. Analytical results can be theoretically achieved in mean field theory in high dimensions or when exact solutions are known such as the two-dimensional Ising model. The theoretical treatment in generic dimensions requires the renormalization group approach or, for systems at thermal equilibrium, the conformal bootstrap techniques. Phase transitions and critical exponents appear in many physical systems such as water at the critical point, in magnetic systems, in sup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Transitions
In physics, chemistry, and other related fields like biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic State of matter, states of matter: solid, liquid, and gas, and in rare cases, plasma (physics), plasma. A phase of a thermodynamic system and the states of matter have uniform physical property, physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. Types of phase transition States of matter Phase transitions commonly refer to when a substance tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous-time Quantum Monte Carlo
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next. This view of time corresponds to a digital clock that gives a fixed reading of 10:37 for a while, and then jumps to a new fixed reading of 10:38, etc. In this framework, each variable of interest is measured once at each time period. The number of measurements between any two time periods is finite. Measurements are typically made at sequential integer values of the variable "time". A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterative Perturbation Theory
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. Mathematics In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exact Diagonalization
Exact diagonalization (ED) is a numerical technique used in physics to determine the eigenstates and energy eigenvalues of a quantum Hamiltonian (quantum mechanics), Hamiltonian. In this technique, a Hamiltonian for a discrete, finite system is expressed in matrix form and Matrix diagonalization, diagonalized using a computer. Exact diagonalization is only feasible for systems with a few tens of particles, due to the exponential growth of the Hilbert space dimension with the size of the quantum system. It is frequently employed to study lattice models, including the Hubbard model, Ising model, Heisenberg model (quantum), Heisenberg model, T-J model, ''t''-''J'' model, and Sachdev-Ye-Kitaev model, SYK model. Expectation values from exact diagonalization After determining the eigenstates , n\rangle and energies \epsilon_n of a given Hamiltonian, exact diagonalization can be used to obtain expectation values of observables. For example, if \mathcal is an observable, its Expectation val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Renormalization Group
The numerical renormalization group (NRG) is a technique devised by Kenneth Wilson to solve certain many-body problems where quantum impurity physics plays a key role. History The numerical renormalization group is an inherently non-perturbative procedure, which was originally used to solve the Kondo model. The Kondo model is a simplified theoretical model which describes a system of magnetic spin-1/2 impurities which couple to metallic conduction electrons (e.g. iron impurities in gold). This problem is notoriously difficult to tackle theoretically, since perturbative techniques break down at low-energy. However, Wilson was able to prove for the first time using the numerical renormalization group that the ground state of the Kondo model is a singlet state. But perhaps more importantly, the notions of renormalization, fixed points, and renormalization group flow were introduced to the field of condensed matter theory — it is for this that Wilson won the Nobel Prize in 1982. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anderson Impurity Model
The Anderson impurity model, named after Philip Warren Anderson, is a Hamiltonian that is used to describe magnetic impurities embedded in metals. It is often applied to the description of Kondo effect-type problems, such as heavy fermion systems and Kondo insulators. In its simplest form, the model contains a term describing the kinetic energy of the conduction electrons, a two-level term with an on-site Coulomb repulsion that models the impurity energy levels, and a hybridization term that couples conduction and impurity orbitals. For a single impurity, the Hamiltonian takes the form :H = \sum_\epsilon_k c^_c_ + \sum_\epsilon_ d^_d_ + Ud^_d_d^_d_ + \sum_V_k(d^_c_ + c^_d_), where the c operator is the annihilation operator of a conduction electron, and d is the annihilation operator for the impurity, k is the conduction electron wavevector, and \sigma labels the spin. The on–site Coulomb repulsion is U, and V gives the hybridization. Regimes The model yields several regi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High-temperature Superconductivity
High-temperature superconductivity (high-c or HTS) is superconductivity in materials with a critical temperature (the temperature below which the material behaves as a superconductor) above , the boiling point of liquid nitrogen. They are "high-temperature" only relative to previously known superconductors, which function only closer to absolute zero. The first high-temperature superconductor was discovered in 1986 by IBM researchers Georg Bednorz and K. Alex Müller. Although the critical temperature is around , this material was modified by Ching-Wu Chu to make the first high-temperature superconductor with critical temperature . Bednorz and Müller were awarded the Nobel Prize in Physics in 1987 "for their important break-through in the discovery of superconductivity in ceramic materials". Most high-c materials are type-II superconductors. The major advantage of high-temperature superconductors is that they can be cooled using liquid nitrogen, in contrast to previously known s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
