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Localization-protected Quantum Order
Many-body localization (MBL) is a dynamical phenomenon which leads to the breakdown of equilibrium statistical mechanics in isolated many-body systems. Such systems never reach local thermal equilibrium, and retain local memory of their initial conditions for infinite times. One can still define a notion of phase structure in these out-of-equilibrium systems. Strikingly, MBL can even enable new kinds of exotic orders that are disallowed in thermal equilibrium – a phenomenon that goes by the name of localization-protected quantum order (LPQO) or eigenstate order Background The study of phases of matter and the transitions between them has been a central enterprise in physics for well over a century. One of the earliest paradigms for elucidating phase structure, associated most with Landau, classifies phases according to the spontaneous breaking of global symmetries present in a physical system. More recently, we have also made great strides in understanding topological phases of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-body Localization
Many-body localization (MBL) is a dynamical phenomenon occurring in isolated many-body quantum systems. It is characterized by the system failing to thermalization, reach thermal equilibrium, and retaining a memory of its initial condition in local observables for infinite times. Thermalization and localization Textbook Quantum statistical mechanics, quantum statistical mechanics assumes that systems go to thermal equilibrium (thermalization). The process of thermalization erases local memory of the initial conditions. In textbooks, thermalization is ensured by coupling the system to an external environment or "reservoir," with which the system can exchange energy. What happens if the system is isolated from the environment, and evolves according to its own Schrödinger equation? Does the system still thermalize? Quantum mechanical time evolution is unitary and formally preserves all information about the initial condition in the quantum state at all times. However, a quant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Equilibrium
Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in thermal equilibrium with itself if the temperature within the system is spatially uniform and temporally constant. Systems in thermodynamic equilibrium are always in thermal equilibrium, but the converse is not always true. If the connection between the systems allows transfer of energy as 'change in internal energy' but does not allow transfer of matter or transfer of energy as work, the two systems may reach thermal equilibrium without reaching thermodynamic equilibrium. Two varieties of thermal equilibrium Relation of thermal equilibrium between two thermally connected bodies The relation of thermal equilibrium is an instance of equilibrium between two bodies, which means that it refers to transfer through a selectively permeable p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spontaneous Symmetry Breaking
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry. Overview By definition, spontaneous symmetry breaking requires the existence of physical laws (e.g. quantum mechanics) which are invariant under a symmetry transformation (such as translation or rotation), so that any pair of outcomes differing only by that transformation have the same probability distribution. For example if measurements of an observable at any two different positions have the same probability distribution, the observable has translational symmetry. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Phases Of Matter
In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition. Various topologically ordered states have interesting properties, such as (1) topological degeneracy and fractional statistics or non-abelian statistics that can be used to realize a topological quantum computer; (2) perfect conducting edge states that may have important device applications; (3) emergent gauge field and Fermi statistics that suggest a quantum information origin of elementary particles; See also (4) topological entanglement entropy th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological Order
In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition. Various topologically ordered states have interesting properties, such as (1) topological degeneracy and fractional statistics or non-abelian statistics that can be used to realize a topological quantum computer; (2) perfect conducting edge states that may have important device applications; (3) emergent gauge field and Fermi statistics that suggest a quantum information origin of elementary particles; See also (4) topological entanglement entropy that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Entanglement
Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics. Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior gives ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mermin–Wagner Theorem
In quantum field theory and statistical mechanics, the Mermin–Wagner theorem (also known as Mermin–Wagner–Hohenberg theorem, Mermin–Wagner–Berezinskii theorem, or Coleman theorem) states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions . Intuitively, this means that long-range fluctuations can be created with little energy cost and since they increase the entropy they are favored. This is because if such a spontaneous symmetry breaking occurred, then the corresponding Goldstone bosons, being massless, would have an infrared divergent correlation function. The absence of spontaneous symmetry breaking in dimensional systems was rigorously proved by David Mermin, Herbert Wagner (1966), and Pierre Hohenberg (1967) in statistical mechanics and by in quantum field theory. That the theorem does not apply to discrete symmetries can be seen in the two-dimensional Ising model. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spontaneous Symmetry Breaking
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry. Overview By definition, spontaneous symmetry breaking requires the existence of physical laws (e.g. quantum mechanics) which are invariant under a symmetry transformation (such as translation or rotation), so that any pair of outcomes differing only by that transformation have the same probability distribution. For example if measurements of an observable at any two different positions have the same probability distribution, the observable has translational symmetry. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-body Localization
Many-body localization (MBL) is a dynamical phenomenon occurring in isolated many-body quantum systems. It is characterized by the system failing to thermalization, reach thermal equilibrium, and retaining a memory of its initial condition in local observables for infinite times. Thermalization and localization Textbook Quantum statistical mechanics, quantum statistical mechanics assumes that systems go to thermal equilibrium (thermalization). The process of thermalization erases local memory of the initial conditions. In textbooks, thermalization is ensured by coupling the system to an external environment or "reservoir," with which the system can exchange energy. What happens if the system is isolated from the environment, and evolves according to its own Schrödinger equation? Does the system still thermalize? Quantum mechanical time evolution is unitary and formally preserves all information about the initial condition in the quantum state at all times. However, a quant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenstate Thermalization Hypothesis
The eigenstate thermalization hypothesis (or ETH) is a set of ideas which purports to explain when and why an isolated Quantum mechanics, quantum mechanical system can be accurately described using equilibrium statistical mechanics. In particular, it is devoted to understanding how systems which are initially prepared in far-from-equilibrium states can evolve in time to a state which appears to be in thermal equilibrium. The phrase "eigenstate thermalization" was first coined by Mark Srednicki in 1994, after similar ideas had been introduced by Josh Deutsch in 1991. The principal philosophy underlying the eigenstate thermalization hypothesis is that instead of explaining the ergodicity of a thermodynamic system through the mechanism of Chaos theory, dynamical chaos, as is done in classical mechanics, one should instead examine the properties of matrix (mathematics), matrix elements of observable quantities in individual stationary state, energy eigenstates of the system. Motivati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anderson Localization
In condensed matter physics, Anderson localization (also known as strong localization) is the absence of diffusion of waves in a ''disordered'' medium. This phenomenon is named after the American physicist P. W. Anderson, who was the first to suggest that electron localization is possible in a lattice potential, provided that the degree of randomness (disorder) in the lattice is sufficiently large, as can be realized for example in a semiconductor with impurities or defects. Anderson localization is a general wave phenomenon that applies to the transport of electromagnetic waves, acoustic waves, quantum waves, spin waves, etc. This phenomenon is to be distinguished from weak localization, which is the precursor effect of Anderson localization (see below), and from Mott localization, named after Sir Nevill Mott, where the transition from metallic to insulating behaviour is ''not'' due to disorder, but to a strong mutual Coulomb repulsion of electrons. Introduction In the or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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