Modeling free anyons at the bosonic and fermionic ends

Vasiuta, Yanina; Rovenchak, Andrij

doi:10.1016/j.physa.2017.09.002

Cited by 6 publications

(3 citation statements)

References 53 publications

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“…Gentile statistics goes back to Bose and Fermi statistics in limit cases. The Gentile system is not just a theoretical model, more and more real systems are found obeying Gentile statistics, such as conjugate annulenes [14] and spin waves of magnetic systems [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A group method solving many-body systems in intermediate statistical representation

Shen,

Zhou,

Dai

et al. 2021

Preprint

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The exact solution of the interacting many-body system is important and is difficult to solve. In this paper, we introduce a group method to solve the interacting many-body problem using the relation between the permutation group and the unitary group. We prove a group theorem first, then using the theorem, we represent the Hamiltonian of the interacting many-body system by the Casimir operators of unitary group. The eigenvalues of Casimir operators could give the exact values of energy and thus solve those problems exactly. This method maps the interacting many-body system onto an intermediate statistical representation. We give the relation between the conjugacy-class operator of permutation group and the Casimir operator of unitary group in the intermediate statistical representation, called the Gentile representation. Bose and Fermi cases are two limitations of the Gentile representation. We also discuss the representation space of symmetric and unitary group in the Gentile representation and give an example of the Heisenberg model to demonstrate this method. It is shown that this method is effective to solve interacting many-body problems.

show abstract

Section: Introductionmentioning

confidence: 99%

A group method solving many-body systems in intermediate statistical representation

Shen,

Zhou,

Dai

et al. 2021

Preprint

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show abstract

“…That is a special algebra we constructed in 2010 [10]. More and more real anyon systems and Gentile systems are observed these decades [11][12][13][14][15]. Fractional statistics are applied in many hot fields of physics.…”

Section: Introductionmentioning

confidence: 99%

Intermediate symmetric construction of transformation between anyon and Gentile statistics

Shen¹,

Zhang²

2021

Commun. Theor. Phys.

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Gentile statistics describes fractional statistical systems in the occupation number representation. Anyon statistics researches those systems in the winding number representation. Both of them are intermediate statistics between Bose–Einstein and Fermi–Dirac statistics. The second quantization of Gentile statistics shows a lot of advantages. According to the symmetry requirement of the wave function and the property of braiding, we give the general construction of transformation between anyon and Gentile statistics. In other words, we introduce the second quantization form of anyons in an easier way. This construction is a correspondence between two fractional statistics and gives a new description of anyon. Basic relations of second quantization operators, the coherent state and Berry phase are also discussed.

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mentioning

confidence: 99%

A group method solving many-body systems in intermediate statistical representation

Shen

Zhou

Dai

et al. 2021

EPL

View full text Add to dashboard Cite

The exact solution of the interacting many-body system is important and is difficult to solve. In this paper, we introduce a group method to solve the interacting many-body problem using the relation between the permutation group and the unitary group. We prove a group theorem first, then using the theorem, we represent the Hamiltonian of the interacting manybody system by the Casimir operators of unitary group. The eigenvalues of Casimir operators could give the exact values of energy and thus solve those problems exactly. This method maps the interacting many-body system onto an intermediate statistical representation. We give the relation between the conjugacy-class operator of permutation group and the Casimir operator of unitary group in the intermediate statistical representation, called the Gentile representation. Bose and Fermi cases are two limitations of the Gentile representation. We also discuss the representation space of symmetric and unitary group in the Gentile representation and give an example of the Heisenberg model to demonstrate this method. It is shown that this method is effective to solve interacting many-body problems.

show abstract

Modeling free anyons at the bosonic and fermionic ends

Cited by 6 publications

References 53 publications

A group method solving many-body systems in intermediate statistical representation

A group method solving many-body systems in intermediate statistical representation

Intermediate symmetric construction of transformation between anyon and Gentile statistics

A group method solving many-body systems in intermediate statistical representation

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