Spin-charge separation
Encyclopedia
In condensed matter physics
, spin–charge separation is an unusual behavior of electron
s in some materials in which they 'split' into two independent particles, the spinon
and the chargon (or its antiparticle, the holon
). The electron can always be theoretically considered as a bound state
of the two, with the spinon carrying the spin
of the electron and the chargon carrying the charge
, but in certain conditions they can become deconfined
and behave as independent particles.
The theory of spin-charge separation originates with the work of Sin-Itiro Tomonaga
who developed an approximate method for treating one-dimensional interacting quantum systems in 1950. This was then developed by Joaquin Mazdak Luttinger
in 1963 with an exactly solvable model which demonstrated spin-charge separation. In 1981 F. Duncan M. Haldane generalized Luttinger's model to the Tomonaga-Luttinger liquid
concept whereby the physics of Luttinger's model was shown theoretically to be a general feature of all one-dimensional metallic systems. Although Haldane treated spinless fermions, the extension to spin-1/2 fermions and associated spin-charge separation was clear so that the promised follow-up paper did not appear.
Spin–charge separation is one of the most unusual manifestations of the concept of quasiparticle
s. This property is counterintuitive, because neither the spinon, with zero charge and spin half, or the chargon, with charge minus one and zero spin, can be constructed as combinations of the electrons, holes
, phonon
s and photon
s that are the constituents of the system. It is an example of fractionalization
, the phenomenon in which the quantum number
s of the quasiparticles are not multiples of those of the elementary particles, but fractions.
Since the original electrons in the system are fermion
s, one of the spinon and chargon has to be a fermion, and the other one has to be a boson
. One is theoretically free to make the assignment in either way, and no observable quantity
can depend on this choice. The formalism with bosonic chargon and fermionic spinion is usually referred to as the "slave–fermion" formalism, while the formalism with fermionic chargon and bosonic spinon is called the "Schwinger boson" formalism. Both approaches have been used for strongly correlated systems, but neither has been proved to be completely successful. One difficulty of the spin–charge separation is that while spinon and chargon are not gauge–invariant quantities, i.e. unphysical objects, there are no direct physical probes to observe them. Therefore more often than not one has to use thermal dynamical or macroscopic techniques to see their effects. This implies that which formalism we choose is irrelevant to real physics, so in principle both approaches should give us the same answer. The reason we obtain radically different answers from these two formalisms is probably because of the wrong mean field solution we choose, which means that we are dealing with the spin–charge separation in a wrong way.
The same theoretical ideas have been applied in the framework of ultracold atom
s. In a two-component Bose gas in 1D, strong interactions can produce a maximal form of spin-charge separation.
and Birmingham
proved experimentally in 2009 that a mass of electrons artificially confined in a small space together will split into spinons and holons due to the intensity of their mutual repulsion (from having the same charge). A team of researchers working at the Advanced Light Source (ALS) of the U.S. Department of Energy’s Lawrence Berkeley National Laboratory also observed peak spectral structures of spin–charge separation around the same time.
Condensed matter physics
Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...
, spin–charge separation is an unusual behavior of electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s in some materials in which they 'split' into two independent particles, the spinon
Spinon
Spinons are one of two quasiparticles, along with holons, that electrons in solids are able to split into during the process of spin–charge separation, when extremely tightly confined at temperatures close to absolute zero....
and the chargon (or its antiparticle, the holon
Holon (physics)
Holons are one of two quasiparticles, along with spinons, that electrons in solids are able to split into during the process of spin–charge separation, when extremely tightly confined at temperatures close to absolute zero.Electrons, being of like charge, repel each other...
). The electron can always be theoretically considered as a bound state
Bound state
In physics, a bound state describes a system where a particle is subject to a potential such that the particle has a tendency to remain localised in one or more regions of space...
of the two, with the spinon carrying the spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
of the electron and the chargon carrying the charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
, but in certain conditions they can become deconfined
Deconfinement
In physics, deconfinement is the property of a phase in which certain particles are allowed to exist as free excitations, rather than only within bound states...
and behave as independent particles.
The theory of spin-charge separation originates with the work of Sin-Itiro Tomonaga
Sin-Itiro Tomonaga
was a Japanese physicist, influential in the development of quantum electrodynamics, work for which he was jointly awarded the Nobel Prize in Physics in 1965 along with Richard Feynman and Julian Schwinger.-Biography:...
who developed an approximate method for treating one-dimensional interacting quantum systems in 1950. This was then developed by Joaquin Mazdak Luttinger
Joaquin Mazdak Luttinger
Joaquin Mazdak Luttinger was an American physicist well-known for his contributions to the theory of interacting electrons in one-dimensional metals and the Fermi-liquid theory...
in 1963 with an exactly solvable model which demonstrated spin-charge separation. In 1981 F. Duncan M. Haldane generalized Luttinger's model to the Tomonaga-Luttinger liquid
Luttinger liquid
A Tomonaga-Luttinger liquid, more often referred to as simply a Luttinger liquid, is a theoretical model describing interacting electrons in a one-dimensional conductor...
concept whereby the physics of Luttinger's model was shown theoretically to be a general feature of all one-dimensional metallic systems. Although Haldane treated spinless fermions, the extension to spin-1/2 fermions and associated spin-charge separation was clear so that the promised follow-up paper did not appear.
Spin–charge separation is one of the most unusual manifestations of the concept of quasiparticle
Quasiparticle
In physics, quasiparticles are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in free space...
s. This property is counterintuitive, because neither the spinon, with zero charge and spin half, or the chargon, with charge minus one and zero spin, can be constructed as combinations of the electrons, holes
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...
, phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
s and photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s that are the constituents of the system. It is an example of fractionalization
Fractionalization
In physics, fractionalization is the phenomenon whereby the quasiparticles of a system cannot be constructed as combinations of its elementary constituents...
, the phenomenon in which the quantum number
Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
s of the quasiparticles are not multiples of those of the elementary particles, but fractions.
Since the original electrons in the system are fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s, one of the spinon and chargon has to be a fermion, and the other one has to be a boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
. One is theoretically free to make the assignment in either way, and no observable quantity
Observable
In physics, particularly in quantum physics, a system observable is a property of the system state that can be determined by some sequence of physical operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value off...
can depend on this choice. The formalism with bosonic chargon and fermionic spinion is usually referred to as the "slave–fermion" formalism, while the formalism with fermionic chargon and bosonic spinon is called the "Schwinger boson" formalism. Both approaches have been used for strongly correlated systems, but neither has been proved to be completely successful. One difficulty of the spin–charge separation is that while spinon and chargon are not gauge–invariant quantities, i.e. unphysical objects, there are no direct physical probes to observe them. Therefore more often than not one has to use thermal dynamical or macroscopic techniques to see their effects. This implies that which formalism we choose is irrelevant to real physics, so in principle both approaches should give us the same answer. The reason we obtain radically different answers from these two formalisms is probably because of the wrong mean field solution we choose, which means that we are dealing with the spin–charge separation in a wrong way.
The same theoretical ideas have been applied in the framework of ultracold atom
Ultracold atom
Ultracold atoms is a term used to describe atoms that are maintained at temperatures close to 0 kelvins , typically below some tenths of microkelvins , where their quantum-mechanical properties become important...
s. In a two-component Bose gas in 1D, strong interactions can produce a maximal form of spin-charge separation.
Observation
Building on physicist F. Duncan M. Haldane's 1981 theory, experts from the Universities of CambridgeUniversity of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
and Birmingham
University of Birmingham
The University of Birmingham is a British Redbrick university located in the city of Birmingham, England. It received its royal charter in 1900 as a successor to Birmingham Medical School and Mason Science College . Birmingham was the first Redbrick university to gain a charter and thus...
proved experimentally in 2009 that a mass of electrons artificially confined in a small space together will split into spinons and holons due to the intensity of their mutual repulsion (from having the same charge). A team of researchers working at the Advanced Light Source (ALS) of the U.S. Department of Energy’s Lawrence Berkeley National Laboratory also observed peak spectral structures of spin–charge separation around the same time.