Equation of state of an anyon gas in a strong magnetic field

Veigy, Alain Dasnières de; Ouvry, Stéphane

doi:10.1103/physrevlett.72.600

Cited by 152 publications

(201 citation statements)

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“…Another derivation of the AB scattering amplitude and of the wave function ne ar the forward direction has been provided by Dasnières de Veigy and Ouvry [7], this time by analyzing the action of the propagator on an incide nt plane wave. The procedure resembles those of [4] and [5], and yields identical results.…”

Section: Introductionmentioning

confidence: 99%

Calculation of the Aharonov-Bohm wave function

Alvarez

1996

Phys. Rev. A

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Section: Introductionmentioning

confidence: 99%

Calculation of the Aharonov-Bohm wave function

Alvarez

1996

Phys. Rev. A

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“…Using the thermodynamic limit prescription (46), the cluster coefficient (45) rewrites, in the thermodynamic limit, as [29] …”

Section: Lll-anyon Thermodynamicsmentioning

confidence: 99%

Anyons and Lowest Landau Level Anyons

Ouvry

2009

The Spin

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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 anyonic 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 AharonovBohm" 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 1 arXiv:0712.2174v1 [cond-mat.stat-mech] 13 Dec 2007 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 Haldane'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...

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“…Let us use our result (83) to evaluate the correlation function of the effective one-family density (23). We shall denote the fluctuating part of ρ(x) in (23) by η(x) = η 1 (x) − 1 λ η 2 (x).…”

Section: Ground-state Wave-functional and Correlation Functionsmentioning

confidence: 99%

“…while m itself satisfies the quadratic equation Finally, note that λ = λ 1 , m = m 1 , subjected to the constraints (22) defining the SOHI, namely, the situation corresponding to (23), is also a solution of (63) and (64).…”

Section: Diagonalization and Dispersion Lawsmentioning

confidence: 99%

“…The CM and its various descendants continue to draw considerable interest due to their diverse physical applications in systems such as random matrices [7], fractional statistics [8]- [11], gravity and black hole physics [12,13], spin chains [14,15], solitons [16]- [20], 2D Yang-Mills theory [21,22], lowest Landau level (LLL) anyon models [23,24], Chern-Simons matrix model [25]- [27], Laughlin-Hall states [28]- [30], and unoriented superstrings in two dimensions [31].…”

Section: Introductionmentioning

confidence: 99%

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Collective field formulation of the multi-species Calogero model and its duality symmetries

2007

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We study the collective field formulation of a restricted form of the multispecies Calogero model, in which the three-body interactions are set to zero. We show that the resulting collective field theory is invariant under certain duality transformations, which interchange, among other things, particles and antiparticles, and thus generalize the well-known strong-weak coupling duality symmetry of the ordinary Calogero model. We identify all these dualities, which form an Abelian group, and study their consequences. We also study the ground state and small fluctuations around it in detail, starting with the two-species model, and then generalizing to an arbitrary number of species.

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Equation of state of an anyon gas in a strong magnetic field

Cited by 152 publications

References 27 publications

Calculation of the Aharonov-Bohm wave function

Calculation of the Aharonov-Bohm wave function

Anyons and Lowest Landau Level Anyons

Collective field formulation of the multi-species Calogero model and its duality symmetries

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