Theoretical model describing interacting fermions in a one-dimensional conductor
Condensed matter physics
Phases
Phase transition
QCP
States of matter
Solid
Liquid
Gas
Plasma
Bose–Einstein condensate
Bose gas
Fermionic condensate
Fermi gas
Fermi liquid
Supersolid
Superfluidity
Luttinger liquid
Time crystal
Phase phenomena
Order parameter
Phase transition
QCP
Electronic phases
Electronic band structure
Plasma
Insulator
Mott insulator
Semiconductor
Semimetal
Conductor
Superconductor
Thermoelectric
Piezoelectric
Ferroelectric
Topological insulator
Spin gapless semiconductor
Electronic phenomena
Quantum Hall effect
Spin Hall effect
Kondo effect
Magnetic phases
Diamagnet
Superdiamagnet
Paramagnet
Superparamagnet Ferromagnet
Antiferromagnet Metamagnet
Spin glass
Quasiparticles
Phonon
Exciton
Plasmon Polariton
Polaron
Magnon
Roton
Soft matter
Amorphous solid
Colloid
Granular material
Liquid crystal
Polymer
Scientists
Van der Waals
Onnes
von Laue
Bragg
Debye
Bloch
Onsager
Mott
Peierls
Landau
Luttinger
Anderson
Van Vleck
Hubbard
Shockley
Bardeen
Cooper
Schrieffer
Josephson
Louis Néel
Esaki
Giaever
Kohn
Kadanoff
Fisher
Wilson
von Klitzing
Binnig
Rohrer
Bednorz
Müller
Laughlin
Störmer
Yang
Tsui
Abrikosov
Ginzburg
Leggett
Parisi
Physics portal
Category
v
t
e
A Luttinger liquid, or Tomonaga–Luttinger liquid, is a theoretical model describing interacting electrons (or other fermions) in a one-dimensional conductor (e.g. quantum wires such as carbon nanotubes).[1] Such a model is necessary as the commonly used Fermi liquid model breaks down for one dimension.
The Tomonaga–Luttinger's liquid was first proposed by Sin-Itiro Tomonaga in 1950. The model showed that under certain constraints, second-order interactions between electrons could be modelled as bosonic interactions. In 1963, J.M. Luttinger reformulated the theory in terms of Bloch sound waves and showed that the constraints proposed by Tomonaga were unnecessary in order to treat the second-order perturbations as bosons. But his solution of the model was incorrect; the correct solution was given by Daniel C. Mattis [de] and Elliot H. Lieb 1965.[2]
^Mattis, Daniel C.; Lieb, Elliot H. (February 1965). Exact solution of a many-fermion system and its associated boson field. Vol. 6. pp. 98–106. Bibcode:1994boso.book...98M. doi:10.1142/9789812812650_0008. ISBN 978-981-02-1847-8. {{cite book}}: |journal= ignored (help)
A Luttingerliquid, or Tomonaga–Luttingerliquid, is a theoretical model describing interacting electrons (or other fermions) in a one-dimensional conductor...
fermions in one dimension, called the Luttingerliquid. Although Luttingerliquids are physically similar to Fermi liquids, the restriction to one dimension...
metals (the electrons in these metals are said to be in a Luttinger-liquid state) and the Fermi-liquid theory. He received his BS and PhD in physics from MIT...
the Fermi liquid theory for electron behavior. Therefore, a 1-D conductor should behave as a Luttingerliquid instead. A Luttingerliquid is a paramagnetic...
Liquid crystal (LC) is a state of matter whose properties are between those of conventional liquids and those of solid crystals. For example, a liquid...
topology. Even less familiar are carbon nanotubes, the quantum wire and Luttingerliquid with their 1-dimensional topologies. Systems with 1D and 2D topologies...
(N/V)^{4/3}} . In 1956, Lev Landau developed the Fermi liquid theory, where he treated the case of a Fermi liquid, i.e., a system with repulsive, not necessarily...
perturbation in a one-dimensional Fermi fluid is modelled by the Tomonaga-Luttingerliquid. The fermions in the fluid that take part in the screening cannot be...
generally unimportant. Soft materials include liquids, colloids, polymers, foams, gels, granular materials, liquid crystals, flesh, and a number of biomaterials...
insulatorsPages displaying short descriptions of redirect targets Quantum spin liquid – Phase of matter Ferromagnetism – Mechanism by which materials form into...
Solid Liquid Gas Plasma Bose–Einstein condensate Bose gas Fermionic condensate Fermi gas Fermi liquid Supersolid Superfluidity Luttingerliquid Time crystal...
term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and...
where superfluidity breaks down. Superfluidity was originally discovered in liquid helium-4 whose atoms are bosons, not fermions. It is far more difficult...
Solid Liquid Gas Plasma Bose–Einstein condensate Bose gas Fermionic condensate Fermi gas Fermi liquid Supersolid Superfluidity Luttingerliquid Time crystal...
substance. Some definitions specify that the particles must be dispersed in a liquid, while others extend the definition to include substances like aerosols...
Solid Liquid Gas Plasma Bose–Einstein condensate Bose gas Fermionic condensate Fermi gas Fermi liquid Supersolid Superfluidity Luttingerliquid Time crystal...
dominates. When the density is intermediate, then it is called granular liquid. Coulomb regarded internal forces between granular particles as a friction...
and microscopic physical properties of matter, especially the solid and liquid phases, that arise from electromagnetic forces between atoms and electrons...
before and after the collision. Condensed matter physics Tomonaga–Luttingerliquid "Discovery About Behavior Of Building Block Of Nature Could Lead To...
order is important in the study of several physical systems such as spin liquids, and the quantum Hall effect, along with potential applications to fault-tolerant...
since been described through phenomenology and microscopic theories. In liquid helium-4, the superfluidity occurs at far higher temperatures than it does...
Solid Liquid Gas Plasma Bose–Einstein condensate Bose gas Fermionic condensate Fermi gas Fermi liquid Supersolid Superfluidity Luttingerliquid Time crystal...
Solid Liquid Gas Plasma Bose–Einstein condensate Bose gas Fermionic condensate Fermi gas Fermi liquid Supersolid Superfluidity Luttingerliquid Time crystal...
interaction that is mediated by conduction electrons. The Tomonaga–Luttingerliquid model approximates second order electron-electron interactions as bosonic...
Solid Liquid Gas Plasma Bose–Einstein condensate Bose gas Fermionic condensate Fermi gas Fermi liquid Supersolid Superfluidity Luttingerliquid Time crystal...
Global Information
