Theory of the ring cyclotron

Fateev, A.P.

doi:10.1088/0368-3281/4/1/110

Cited by 3 publications

(6 citation statements)

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“…We look carefully at Belavin Polyakov [10] n-skyrmion static classical solutions. The mathematical structure of the n-skyrmion solution in one particular parameterization readily suggests that each skyrmion is made of 2n 'constituent point particles [7,11,12].To understand the quantum dynamics of these constituent particles we construct the skyrmion operator for our spin-1 2 Heisenberg antiferromagnet and discover that the creation operator for these constituent particles have mathematical structure similar to Laughlin's quasi hole and quasi particle operators of quantum Hall effect. By a Berry phase analysis we show their spin to be half.…”

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Spinon deconfinement above a finite energy gap in two-dimensional quantum Heisenberg antiferromagnets

Baskaran

2003

Phys. Rev. B

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The familiar spin-1 2 quantum Heisenberg antiferromanget in a 2d square lattice is shown, within the non linear sigma model approximations, to be another novel state of matter that has excitations with fractional quantum numbers above a finite energy gap. The 1-skyrmion with an energy ≈ 2πJ is shown to be made of two 'deconfined spinons' or 'SU(2) vortices'. The many skyrmion operator and the wave functions that we have found are strikingly similar to quantum Hall quasi particle operators and wave functions. We also predict the presence of finite energy 'spin-S spinon' for a general spin-S Heisenberg antiferromagnets in 2d. Some consequences are briefly discussed. ' [7] are the 'deconfined' spinons based on some heuristic arguments.Recent inelastic neutron scattering results covering a large energy and momentum range in the insulating cuprates [8], and also Raman [9] and infrared measurements also makes the search for any signatures of spinons at low and high energies very meaningful and urgent.The aim of the present letter is to study the spectrum of quantum Heisenberg antiferromagnet in 2d and look for deconfined spinons above a finite energy gap, within the O(3) non linear sigma (NLS) model approach. We look carefully at Belavin Polyakov [10] n-skyrmion static classical solutions. The mathematical structure of the n-skyrmion solution in one particular parameterization readily suggests that each skyrmion is made of 2n 'constituent point particles [7,11,12].To understand the quantum dynamics of these constituent particles we construct the skyrmion operator for our spin-1 2 Heisenberg antiferromagnet and discover that the creation operator for these constituent particles have mathematical structure similar to Laughlin's quasi hole and quasi particle operators of quantum Hall effect. By a Berry phase analysis we show their spin to be half. Asymptotic form of the modulus of the n-skyrmion wave function in terms of collective coordinates is also found.Our starting point is the spin-S quantum Heisenberg antiferromagnet in a 2d square lattice with nearest neighbor interactions. Following the standard derivation [13] one arrives at the O(3) NLS model action along with the important lattice sum of Berry phases:Here µ = x, y and n(r) is a normalized (n(r) · n(r) = 1) sub lattice magnetization vector. The coefficient ρ 0 ≈ J for S = 1 2 case, and v s is the spin wave velocity. The Berry phase term is a lattice sumHere the integers (m,n) stand for a lattice site and Ω o (n m,n ) = dt du 8π n m.n · (∂ t n m.n × ∂ u n m.n ) is the single site Berry phase.Inspired by the conjecture of reference (6) we look at the finite energy topological solutions in our search for spinons. The multi skyrmion solutions found by Belavin and Polyakov [10] An n-skyrmion solution is given byHere z = x + iy. The n complex co-ordinates a i and b i characterize the skyrmion solution. The function w(z) and the sub lattice magnetization n(r) ≡ (sin φ(r) cos θ(r), sin φ(r) sin θ(r), cos φ(r)) are related by w(z) ≡ cot φ(r) 2 e iθ(r)The n-antisk...

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Spinon deconfinement above a finite energy gap in two-dimensional quantum Heisenberg antiferromagnets

Baskaran

2003

Phys. Rev. B

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“…In the radially symmetric field configuration (7), the reduced Bogomol'nyi (self-or antiself-dual) equation and the topological charge density of the resulting 1-dimensional subsystem corresponding to (4) and (5)…”

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Dilute instanton gas of an O(3) Skyrme model

et al. 1998

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The pure-Skyrme limit of a scale-breaking Skyrmed O(3) sigma model in 1+1 dimensions is employed to study the effect of the Skyrme term on the semiclassical analysis of a field theory with instantons. The instantons of this model are self-dual and can be evaluated explicitly. They are also localised to an absolute scale, and their fluctuation action can be reduced to a scalar subsystem. This permits the explicit calculation of the fluctuation determinant and the shift in vacuum energy due to instantons. The model also illustrates the semiclassical quantisation of a Skyrmed field theory.

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“…For answering the question in the first paragraph, a semiclassical path integral can be computed in the dual theory and compared with analogous calculations for the O(3) nonlinear σ−model. (For example, one can try to reproduce the results of Fateev, Frolov and Schwarz [8] in the dual theory.) We plan to report on these calculations in a forthcoming article.…”

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“…We first reproduce the equations (6), (7) and (8). For the equations of motion resulting from variations of χ, we can ignore the BF -term.…”

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