Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Thermal Correlators of Anyons in Two Dimensions

N. Ilieva, H. Narnhofer, W. Thirring, H. Narnhofer, W. Thirring

Published Jan 1, 1999• 3 citations
OpenAlex

Abstract

for Mathematical Physics Abstract The anyon fields have trivial ff-commutator for ff not integer. For integer ff the commutators become temperature-dependent operator valued distributions. The n-point functions do not factorize as for quasifree states. MSC-class: 81T05, 81T40, 82B10, 82B23 Keywords: two-dimensional models, fractional statistics, KMS states,

Related papers

Thermal correlators of anyons in two dimensions

N Ilieva, H Narnhofer, W Thirring

The anyon fields have a trivial α-commutator for α not integer. For integer α the commutators become temperature-dependent operator-valued distributions. The n -point functions do not factorize as for quasifree states.

arXiv:math-ph/0004006•Journal of Physics A Mathematical and General•Mar 30, 2001•1 citation

Laughlin type wave function for two-dimensional anyon fields in a KMS-state

Nevena Ilieva, W. Thirring

The correlation functions of two-dimensional anyon fields in a KMS-state are studied. The n-particle wave functions of noncanonical fermions of level , odd, are shown to be of Laughlin type of order . For the first noncanonical Fermi class (=3) this is simply the finite-temperature generalization of Laughlin wave function. This relates the rst and second quantized pictures of the fractional quantum Hall effect.

•Jan 1, 2000•5 citations

Temperature correlators in the one-dimensional Hubbard model in the strong coupling limit

A. G. Izergin, A. G. Pronko, N. I. Abarenkova

We consider the one-dimensional Hubbard model with the infinitely strong repulsion. The two-point dynamical temperature correlation functions are calculated. They are represented as Fredholm determinants of linear integrable integral operators. 1 Introduction The one-dimensional Hubbard model [1] is one of the most interesting and important model of strongly correlated electrons (see, e.g., book [2]). The hamiltonian of the model with the chemical potential h in the external constant field B describes interacting fermions on the one-dimensional periodic lattice of length L: HU = \\Gamma L X x=1 X ff=";# i c y x;ff c x\\Gamma1;ff + c y x\\Gamma1;ff c x;ff j +h L X x=1 (n x;" + n x;# ) \\Gamma B L X x=1 (n x;" \\Gamma n x;# ) + U L X x=1 n x;" n x;# : (1) Here c x;ff and c y x;ff (x = 1; . . . ; L; ff ="; #; c 0;ff j c L;ff ; c y 0;ff j c y L;ff ) are canonical fermion fields with the anticommutation relations [c x;ff ; c y y;fi ] + = ffi x;y ffi ff;fi ...

•Jan 1, 1998•22 citations

One-dimensional impenetrable anyons in thermal equilibrium: IV. Large time and distance asymptotic behavior of the correlation functions

Ovidiu I Pâţu, V. E. Korepin, D. V. Averin

This work presents the derivation of the large time and distance asymptotic behavior of the field-field correlation functions of impenetrable one-dimensional anyons at finite temperature. In the appropriate limits of the statistics parameter, we recover the well-known results for impenetrable bosons and free fermions. In the low-temperature (usually expected to be the "conformal") limit, and for all values of the statistics parameter away from the bosonic point, the leading term in the correlator does not agree with the prediction of the conformal field theory, and is determined by the singularity of the density of the single-particle states at the bottom of the single-particle energy spectrum.

arXiv:0912.3633•Journal of Physics A Mathematical and Theoretical•Mar 2, 2010•26 citations

Anyons and Lowest Landau Level Anyons

Stéphane Ouvry

Intermediate statistics interpolating from Bose statistics to Fermi statistics are allowed in two dimensions. This is due to the particular topology of the two dimensional configuration space of identical particles, leading to non trivial braiding of particles around each other. One arrives at quantum many-body states with a multivalued phase factor, which encodes the any- onic nature of particle windings. Bosons and fermions appear as two limiting cases. Gauging away the phase leads to the so-called anyon model, where the charge of each particle interacts “à la Aharonov-Bohm” with the fluxes carried by the other particles. The multivaluedness of the wave function has been traded off for topological interactions between ordinary particles. An alternative Lagrangian formulation uses a topological Chern-Simons term in 2+1 dimensions. Taking into account the short distance repulsion between particles leads to an Hamiltonian well defined in perturbation theory, where all perturbative divergences have disappeared. Together with numerical and semi-classical studies, perturbation theory is a basic analytical tool at disposal to study the model, since finding the exact N-body spectrum seems out of reach (except in the 2-body case which is solvable, or for particular classes of N-body eigenstates which generalize some 2-body eigenstates). However, a simplification arises when the anyons are coupled to an external homogeneous magnetic field. In the case of a strong field, by projecting the system on its lowest Landau level (LLL, thus the LLL-anyon model), the anyon model becomes solvable, i.e., the classes of exact eigenstates alluded to above provide for a complete interpolation from the LLL-Bose spectrum to the LLL-Fermi spectrum. Being a solvable model allows for an explicit knowledge of the equation of state and of the mean occupation number in the LLL, which do interpolate from the Bose to the Fermi cases. It also provides for a combinatorial interpretation of LLL-anyon braiding statistics in terms of occupation of single particle states. The LLL-anyon model might also be relevant experimentally: a gas of electrons in a strong magnetic field is known to exhibit a quantized Hall conductance, leading to the integer and fractional quantum Hall effects. Haldane/exclusion statistics, introduced to describe FQHE edge excitations, is a priori different from anyon statistics, since it is not defined by braiding considerations, but rather by counting arguments in the space of available states. However, it has been shown to lead to the same kind of thermodynamics as the LLL-anyon thermodynamics (or, in other words, the LLL-anyon model is a microscopic quantum mechanical realization of Hal- dane’s statistics). The one dimensional Calogero model is also shown to have the same kind of thermodynamics as the LLL-anyons thermodynamics. This is not a coincidence: the LLL-anyon model and the Calogero model are intimately related, the latter being a particular limit of the former. Finally, on the purely combinatorial side, the minimal difference partition problem — partition of integers with minimal difference constraints on their parts — can also be mapped on an abstract exclusion statistics model with a constant one-body density of states, which is neither the LLL-anyon model nor the Calogero model. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

arXiv:0712.2174•Birkhäuser Basel eBooks•Jan 1, 2009•32 citations

Statistical phases and momentum spacings for one-dimensional anyons

Martin Greiter

Anyons and fractional statistics are by now well established in two-dimensional systems. In one dimension, fractional statistics has been established so far only through Haldane's fractional exclusion principle, but not via a fractional phase the wave function acquires as particles are interchanged. At first sight, the topology of the configuration space appears to preclude such phases in one dimension. Here we argue that the crossings of one-dimensional anyons are always unidirectional, which makes it possible to assign phases consistently and hence to introduce a statistical angle $\ensuremath{\theta}$. The fractional statistics then manifests itself in fractional spacings of the single-particle momenta of the anyons when periodic boundary conditions are imposed. These spacings are given by $\ensuremath{\Delta}p=2\ensuremath{\pi}\ensuremath{\hbar}/L(|\ensuremath{\theta}|/\ensuremath{\pi}+\text{non-negative}\text{ }\text{integer})$ for a system of length $L$. This condition is the analog of the quantization of relative angular momenta according to ${l}_{\text{z}}=\ensuremath{\hbar}(\ensuremath{-}\ensuremath{\theta}/\ensuremath{\pi}+2\ifmmode\times\else\texttimes\fi{}\text{integer})$ for two-dimensional anyons.

arXiv:0707.1011•Physical Review B•Feb 11, 2009•43 citations
for Mathematical Physics Abstract The anyon fields have trivial ff-commutator for ff not integer. For integer ff the commutators become temperature-dependent operator valued distributions. The n-point functions do not factorize as for quasifree states. MSC-class: 81T05, 81T40, 82B10, 82B23 Keywords: two-dimensional models, fractional statistics, KMS states,
We consider the one-dimensional Hubbard model with the infinitely strong repulsion. The two-point dynamical temperature correlation functions are calculated. They are represented as Fredholm determinants of linear integrable integral operators. 1 Introduction The one-dimensional Hubbard model [1] is one of the most interesting and important model of strongly correlated electrons (see, e.g., book [2]). The hamiltonian of the model with the chemical potential h in the external constant field B describes interacting fermions on the one-dimensional periodic lattice of length L: HU = \\Gamma L X x=1 X ff=";# i c y x;ff c x\\Gamma1;ff + c y x\\Gamma1;ff c x;ff j +h L X x=1 (n x;" + n x;# ) \\Gamma B L X x=1 (n x;" \\Gamma n x;# ) + U L X x=1 n x;" n x;# : (1) Here c x;ff and c y x;ff (x = 1; . . . ; L; ff ="; #; c 0;ff j c L;ff ; c y 0;ff j c y L;ff ) are canonical fermion fields with the anticommutation relations [c x;ff ; c y y;fi ] + = ffi x;y ffi ff;fi ...
This work presents the derivation of the large time and distance asymptotic behavior of the field-field correlation functions of impenetrable one-dimensional anyons at finite temperature. In the appropriate limits of the statistics parameter, we recover the well-known results for impenetrable bosons and free fermions. In the low-temperature (usually expected to be the "conformal") limit, and for all values of the statistics parameter away from the bosonic point, the leading term in the correlator does not agree with the prediction of the conformal field theory, and is determined by the singularity of the density of the single-particle states at the bottom of the single-particle energy spectrum.
Intermediate statistics interpolating from Bose statistics to Fermi statistics are allowed in two dimensions. This is due to the particular topology of the two dimensional configuration space of identical particles, leading to non trivial braiding of particles around each other. One arrives at quantum many-body states with a multivalued phase factor, which encodes the any- onic nature of particle windings. Bosons and fermions appear as two limiting cases. Gauging away the phase leads to the so-called anyon model, where the charge of each particle interacts “à la Aharonov-Bohm” with the fluxes carried by the other particles. The multivaluedness of the wave function has been traded off for topological interactions between ordinary particles. An alternative Lagrangian formulation uses a topological Chern-Simons term in 2+1 dimensions. Taking into account the short distance repulsion between particles leads to an Hamiltonian well defined in perturbation theory, where all perturbative divergences have disappeared. Together with numerical and semi-classical studies, perturbation theory is a basic analytical tool at disposal to study the model, since finding the exact N-body spectrum seems out of reach (except in the 2-body case which is solvable, or for particular classes of N-body eigenstates which generalize some 2-body eigenstates). However, a simplification arises when the anyons are coupled to an external homogeneous magnetic field. In the case of a strong field, by projecting the system on its lowest Landau level (LLL, thus the LLL-anyon model), the anyon model becomes solvable, i.e., the classes of exact eigenstates alluded to above provide for a complete interpolation from the LLL-Bose spectrum to the LLL-Fermi spectrum. Being a solvable model allows for an explicit knowledge of the equation of state and of the mean occupation number in the LLL, which do interpolate from the Bose to the Fermi cases. It also provides for a combinatorial interpretation of LLL-anyon braiding statistics in terms of occupation of single particle states. The LLL-anyon model might also be relevant experimentally: a gas of electrons in a strong magnetic field is known to exhibit a quantized Hall conductance, leading to the integer and fractional quantum Hall effects. Haldane/exclusion statistics, introduced to describe FQHE edge excitations, is a priori different from anyon statistics, since it is not defined by braiding considerations, but rather by counting arguments in the space of available states. However, it has been shown to lead to the same kind of thermodynamics as the LLL-anyon thermodynamics (or, in other words, the LLL-anyon model is a microscopic quantum mechanical realization of Hal- dane’s statistics). The one dimensional Calogero model is also shown to have the same kind of thermodynamics as the LLL-anyons thermodynamics. This is not a coincidence: the LLL-anyon model and the Calogero model are intimately related, the latter being a particular limit of the former. Finally, on the purely combinatorial side, the minimal difference partition problem — partition of integers with minimal difference constraints on their parts — can also be mapped on an abstract exclusion statistics model with a constant one-body density of states, which is neither the LLL-anyon model nor the Calogero model. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Anyons and fractional statistics are by now well established in two-dimensional systems. In one dimension, fractional statistics has been established so far only through Haldane's fractional exclusion principle, but not via a fractional phase the wave function acquires as particles are interchanged. At first sight, the topology of the configuration space appears to preclude such phases in one dimension. Here we argue that the crossings of one-dimensional anyons are always unidirectional, which makes it possible to assign phases consistently and hence to introduce a statistical angle $\ensuremath{\theta}$. The fractional statistics then manifests itself in fractional spacings of the single-particle momenta of the anyons when periodic boundary conditions are imposed. These spacings are given by $\ensuremath{\Delta}p=2\ensuremath{\pi}\ensuremath{\hbar}/L(|\ensuremath{\theta}|/\ensuremath{\pi}+\text{non-negative}\text{ }\text{integer})$ for a system of length LLL. This condition is the analog of the quantization of relative angular momenta according to ${l}_{\text{z}}=\ensuremath{\hbar}(\ensuremath{-}\ensuremath{\theta}/\ensuremath{\pi}+2\ifmmode\times\else\texttimes\fi{}\text{integer})$ for two-dimensional anyons.