Anyons

Myrheim, Jan

doi:10.1007/3-540-46637-1_4

Cited by 16 publications

(12 citation statements)

References 249 publications

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“…In particular, the lower bound in (3) depends on α as √ α * = ν −1/2 for small odd-numerator fractions and tends to zero with N for even-numerator and irrational numbers. In addition to the above, for an arbitrary state Ψ with fixed total angular momentum L ∈ Z one also has the bound [50,51,13]…”

Section: The Many-anyon Ground-state Energymentioning

confidence: 99%

“…At this point one might worry about actually computing (or at least bounding) the energy of the proposed trial states. Fortunately, however, it turns out that ψ α given in (8) for even-numerator α is an exact (but singular) eigenfunction of the harmonic oscillator HamiltonianĤ N with (see [78][79][80]13]…”

Section: Ideal Anyons In a Harmonic Trapmentioning

confidence: 99%

“…This is then called the 'magnetic gauge picture' for anyons. We refer to the extensive reviews [7][8][9][10][11][12][13][14][15][16] for a more complete background on the topic.…”

Section: Introductionmentioning

confidence: 99%

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Many-anyon trial states

Lundholm

2017

Phys. Rev. A

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Section: The Many-anyon Ground-state Energymentioning

confidence: 99%

Section: Ideal Anyons In a Harmonic Trapmentioning

confidence: 99%

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Many-anyon trial states

Lundholm

2017

Phys. Rev. A

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“…[55,56] for a system of two anyons in the presence of the Coulomb potential), while for three or more particles only part of the spectrum is known exactly. The three-and four-anyon spectra have been investigated by means of numerical diagonalization techniques [57][58][59][60], and a subspace of exact eigenstates is also known analytically for arbitrary N [61][62][63][64][65]. Rigorous upper and lower bounds on the exact ground-state energy were established in Refs.…”

Section: A Regular Anyon Hamiltonianmentioning

confidence: 99%

Quantum impurity model for anyons

et al. 2020

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“…Besides bosonic and fermionic statistics, a continuous family of intermediate statistics serves to explain important effects involved in two or one dimensional physics. Remarkably, in D = 2, excitations in the fractional quantum Hall effect can be described as anyons 1,2 . Onedimensional systems can occur either because only onedimensional dynamics is allowed in the system (even if the system lives in higher dimensions) or because the samples are indeed one-dimensional (like quantum wires, carbon nanotubes, systems with charge density wave order, etc).…”

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Fermionic long-range correlations realized by particles obeying deformed statistics

Osterloh

Amico

Eckern

2000

J. Phys. A: Math. Gen.

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Deformed exchange statistics is realized in terms of electronic operators. This is employed to rewrite Hubbard type lattice models for particles obeying deformed statistics (we refer to them as deformed models) as lattice models for electrons. The resulting models show up gauge-like modulations in the hopping processes, which induce long-range correlations in the lattice. The conditions for the Bethe ansatz solvability of the latter are interpreted as restrictions imposed on the statistics to be compatible with the Bethe ansatz solvability of the deformed models. It is found that solvable deformed models are not unitarily equivalent to fermionic models if the exchange of particles with the same spin-orientations is deformed. Statistics deformations, where the exchange relation of two particles is influenced by the presence of other particles, cannot be realized by fermionic operators.The statistics of degrees of freedom drastically affects the physical properties of a many-particle system. Besides bosonic and fermionic statistics, a continuous family of intermediate statistics serves to explain important effects involved in two or one dimensional physics. Remarkably, in D = 2, excitations in the fractional quantum Hall effect can be described as anyons 1,2 . Onedimensional systems can occur either because only onedimensional dynamics is allowed in the system (even if the system lives in higher dimensions) or because the samples are indeed one-dimensional (like quantum wires, carbon nanotubes, systems with charge density wave order, etc). In the present paper we shall focus on deformed statistics in one dimension. Defining arbitrary statistics in one dimension exhibits several peculiarities 3 . In particular, imposing the statistics in one dimension can be interpreted as a "continuity condition" on the wave function (arising from the set of coordinates such that two or more particles coincide), fixing its symmetry. One dimensional fractional statistics arises since this constraint on the wave function can be imposed arbitrarily. Explicit realizations of 1D fractional statistics quasi particles, formulated in "first quantization", are the eigenstates of Calogero-Sutherland models.In Refs. 4 and 5, the notion of Deformed Exchange Statistics (DES) was defined as a specific deformation of electronic commutation rules (in second quantization). Mathematical aspects of this type of statistics have been also studied in Refs. 6,7. We applied DES to investigate how robust is the solvability by Coordinate Bethe Ansatz (CBA) 8,9 of the XXZ and the Hubbard model with respect to such a modification of the particle content (we have called those DES preserving CBA solvability Solvable DES). In the present paper we show that the solvable deformed Hubbard model (without Schulz-Shastry type correlations) is equivalent to adding correlations similar to those discussed by Schulz and Shastry 10 to the undeformed Hubbard model. We prove this realizing DES operators by composites of electronic operators. Using the results of Ref. 11 we ...

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Anyons

Cited by 16 publications

References 249 publications

Many-anyon trial states

Many-anyon trial states

Quantum impurity model for anyons

Fermionic long-range correlations realized by particles obeying deformed statistics

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