Bosonic end perturbative calculations for quantum mechanical anyon systems require a regularization. I regularize by adding a specific $\\delta$ -function potential to the Hamiltonian. The reliability of this regularization procedure is verified by comparing its results for the 2-anyon in harmonic potential system with the known exact solutions. I then use the $\\delta$ -function regularized bosonic end perturbation theory to test some recent conjectures concerning the unknown portion of the many-anyon spectra.Bosonic end perturbative calculations for quantum mechanical anyon systems require a regularization. I regularize by adding a specific $\\delta$-function potential to the Hamiltonian. The reliability of this regularization procedure is verified by comparing its results for the 2-anyon in harmonic potential system with the known exact solutions. I then use the $\\delta$-function regularized bosonic end perturbation theory to test some recent conjectures concerning the unknown portion of the many-anyon spectra.

Jan 1, 199411 citations

An introduction to anyons

Diptiman Sen

PramanaJul 1, 19935 citations

The Existence of Anyons

Ijaz Durrani

Jan 1, 20260 citations

Perturbative renormalizations of anyon quantum mechanics

Giovanni Amelino-camelia A

In bosonic and perturbative calculations for quantum mechanical anyon systems a regularization and renormalization procedure, analogous to those used in field theory, is necessary. I examine the reliability and the physical interpretation of the most commonly used bosonic end regularization procedures. I then use the regularization procedure with the most transparent physical intepretation to derive some bosnic end perturbation theory results on anyon spectra, including a three-anyon ground state energy.In bosonic and perturbative calculations for quantum mechanical anyon systems a regularization and renormalization procedure, analogous to those used in field theory, is necessary. I examine the reliability and the physical interpretation of the most commonly used bosonic end regularization procedures. I then use the regularization procedure with the most transparent physical intepretation to derive some bosnic end perturbation theory results on anyon spectra, including a three-anyon ground state energy.

arXiv:hep-th/9406212Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsFeb 15, 199519 citations

Quantum simulation of lattice gauge theories coupled to fermionic matter via anyonic regularization

Mason L. Rhodes, Shivesh Pathak, Riley W. Chien

The optimal regularization of infinite-dimensional gauge-field degrees of freedom is a central open problem in the simulation of lattice gauge theories on quantum computers. Here, we consider regularizing the gauge field by replacing the gauge group $G$ with a braided fusion category whose objects correspond to Wilson lines of the associated Chern-Simons theory $G_k$ , with the level $k$ serving as the regularization parameter. We demonstrate how to couple these regularized gauge groups to fermionic matter using the framework of fusion surface models, which treats matter and gauge field excitations as interacting anyons. We then address the simulation of the regularized Hamiltonian, in the Kogut-Susskind formulation, on fault-tolerant quantum computers. We provide explicit quantum circuit constructions for implementing the primitive gates in this model, the $F$ and $R$ symbols, for $U(1)_k$ and $SU(2)_k$ anyon theories.The optimal regularization of infinite-dimensional gauge-field degrees of freedom is a central open problem in the simulation of lattice gauge theories on quantum computers. Here, we consider regularizing the gauge field by replacing the gauge group $G$ with a braided fusion category whose objects correspond to Wilson lines of the associated Chern-Simons theory $G_k$, with the level $k$ serving as the regularization parameter. We demonstrate how to couple these regularized gauge groups to fermionic matter using the framework of fusion surface models, which treats matter and gauge field excitations as interacting anyons. We then address the simulation of the regularized Hamiltonian, in the Kogut-Susskind formulation, on fault-tolerant quantum computers. We provide explicit quantum circuit constructions for implementing the primitive gates in this model, the $F$ and $R$ symbols, for $U(1)_k$ and $SU(2)_k$ anyon theories.

quant-pharXiv:2603.15820Mar 18, 20260 citations

Second virial coefficient for contact-interacting anyons

Paola Giacconi A, Fabio Maltoni B, Roberto Soldati

We study the thermodynamic properties of the anyon gas in the presence of a contact interaction. In particular, we use dimensional and analytical regularizations to calculate the second virial coefficient for free and contact-interacting anyons. The Bethe-Uhlenbeck formula is discussed and it is shown that the same result is regained using the \ensuremath{\zeta} regularization. Finally, the second virial coefficients for contact-interacting particles in two and three spatial dimensions are obtained as special cases. \textcopyright{} 1996 The American Physical Society.We study the thermodynamic properties of the anyon gas in the presence of a contact interaction. In particular, we use dimensional and analytical regularizations to calculate the second virial coefficient for free and contact-interacting anyons. The Bethe-Uhlenbeck formula is discussed and it is shown that the same result is regained using the \ensuremath{\zeta} regularization. Finally, the second virial coefficients for contact-interacting particles in two and three spatial dimensions are obtained as special cases. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matterApr 15, 199614 citations

Bosonic end perturbative calculations for quantum mechanical anyon systems require a regularization. I regularize by adding a specific

\\delta

-function potential to the Hamiltonian. The reliability of this regularization procedure is verified by comparing its results for the 2-anyon in harmonic potential system with the known exact solutions. I then use the

\\delta

-function regularized bosonic end perturbation theory to test some recent conjectures concerning the unknown portion of the many-anyon spectra.

G

with a braided fusion category whose objects correspond to Wilson lines of the associated Chern-Simons theory

G_k

, with the level

k

serving as the regularization parameter. We demonstrate how to couple these regularized gauge groups to fermionic matter using the framework of fusion surface models, which treats matter and gauge field excitations as interacting anyons. We then address the simulation of the regularized Hamiltonian, in the Kogut-Susskind formulation, on fault-tolerant quantum computers. We provide explicit quantum circuit constructions for implementing the primitive gates in this model, the

F

and

R

symbols, for

U(1)_k

and

SU(2)_k

anyon theories.