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

Journal of the Physical Society of Japan

Explicit Construction of the Second-Quantized Anyon Operators

Kiyoshi Sogo

Published Jul 15, 1995• 1 citation
Publisher

Abstract

Creation and annihilation operators of anyons are constructed explicitly by using vertex operators for the Calogero-Sutherland-Moser model.
DOI
10.1143/jpsj.64.2249

Related papers

Spin-dependent extension of Calogero-Sutherland model through anyon-like representations of permutation operators

B. Basu-Mallick

arXiv:hep-th/9602107•Nuclear Physics B•Dec 1, 1996•26 citations

Constructing and Deconstructing Non-Abelian Anyons

Bel 'en Paredes

Bulletin of the American Physical Society•Mar 2, 2015•0 citations

Second quantization of the elliptic Calogero-Sutherland model

Edwin Langmann A

We construct a quantum field theory model of anyons on a circle and at finite temperature. We find an anyon Hamiltonian providing a second quantization of the elliptic Calogero-Sutherland model. This allows us to prove a remarkable identity which is a starting point for an algorithm to construct eigenfunctions and eigenvalues of the elliptic Calogero-Sutherland Hamiltonian.

•Jan 1, 2001•13 citations

Modeling free anyons at the bosonic and fermionic ends

Yanina Vasiuta, Andrij A. Rovenchak

arXiv:1706.00032•Physica A Statistical Mechanics and its Applications•Sep 7, 2017•7 citations

Calogero-Sutherland model in interacting fermion picture and explicit construction of Jack states

Jian-Feng Wu, Ming Yu

The 40-year-old Calogero-Sutherland (CS) model remains a source of inspirations for understanding 1d interacting fermions. At $β=1, \text{or}0$, the CS model describes a free non-relativistic fermion, or boson theory, while for generic $β$, the system can be interpreted either as interacting fermions or bosons, or free anyons depending on the context. However, we shall show in this letter that the fermionic picture is advantageous in diagonalizing the CS Hamiltonian. Comparing to the previously known multi-integral representation or the Dunkl operator formalism for the CS wave functions, our method depends on the (upper or lower) triangular nature of the fermion interaction, which is resolved in perturbation theory of the second quantized form. The eigenstate is constructed from a multiplet of unperturbed states and the perturbation is of finite order. The full construction is a similarity transformation from the free fermion theory, in the same spirit as the Landau Fermi liquid theory and the 1d Luttinger liquid theory. That means quasi-particles or anyons can be represented in terms of free fermion modes (or bosonic modes via bosonization). The method is applicable to other (higher than one space dimension) systems for which the adiabatic theorem applies.

arXiv:1110.6720•Oct 31, 2011•4 citations

Exact diagonalization of 1D interacting spinless Fermions

Heiner Kohler

We acquire a method of constructing an infinite set of exact eigenfunctions of 1D interacting spinless Fermionic systems. Creation and annihilation operators for the interacting system are found and thereby the many-body Hamiltonian is diagonalized. The formalism is applied to several examples. One example is the theory of Jack polynomials. For the Calogero–Moser–Sutherland Hamiltonian a direct proof is given that the asymptotic Bethe ansatz is correct.

arXiv:0801.0132•Journal of Mathematical Physics•Mar 1, 2011•4 citations
The 40-year-old Calogero-Sutherland (CS) model remains a source of inspirations for understanding 1d interacting fermions. At β=1,or0β=1, \text{or}0β=1,or0, the CS model describes a free non-relativistic fermion, or boson theory, while for generic βββ, the system can be interpreted either as interacting fermions or bosons, or free anyons depending on the context. However, we shall show in this letter that the fermionic picture is advantageous in diagonalizing the CS Hamiltonian. Comparing to the previously known multi-integral representation or the Dunkl operator formalism for the CS wave functions, our method depends on the (upper or lower) triangular nature of the fermion interaction, which is resolved in perturbation theory of the second quantized form. The eigenstate is constructed from a multiplet of unperturbed states and the perturbation is of finite order. The full construction is a similarity transformation from the free fermion theory, in the same spirit as the Landau Fermi liquid theory and the 1d Luttinger liquid theory. That means quasi-particles or anyons can be represented in terms of free fermion modes (or bosonic modes via bosonization). The method is applicable to other (higher than one space dimension) systems for which the adiabatic theorem applies.