Spinon excitations in the<i>XX</i>chain: spectra, transition rates, observability

Arikawa, Mitsuhiro; Karbach, Michael; Müller, Gerhard; Wiele, Klaus

doi:10.1088/0305-4470/39/34/002

Cited by 18 publications

(34 citation statements)

References 22 publications

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“…(i) Consider the vertical lines dividing the space of the I 1 α into two domains, the inside and the outside, the latter wrapping around at ±N/2. (ii) Every I figure 6 establishes the much needed link between spinon motif of the fermion representation at ∆ = 0 introduced in [13,14] and the spinon motif of the string representation at ∆ = 1 introduced in figure 5. Unlike the solitons at ∆ → ∞, the spinons at ∆ = 0 are not free.…”

Section: Limit: Broken Strings Fermions and Spinonsmentioning

confidence: 83%

“…The second term in (13) ensures that the set {I i } remains the same as an eigenstate is tracked across the axial regime [7]. Here x is the floor function (integer part of x).…”

Section: Axial Regimementioning

confidence: 99%

“…are statistical capacity constants and statistical interaction coefficients, respectively, that are specific to the string particles [13,18,[24][25][26]. Taking into account the (2S T + 1)-fold degeneracy of each multiplet, this classification accounts for the complete spectrum,…”

Section: Limit: Strings and Spinonsmentioning

confidence: 99%

“…These multiplets split up energetically at ∆ = 1. At ∆ = 0 the energy levels join up in new degenerate configurations, reflecting different symmetries [12][13][14][15][16][17]. A more natural classification scheme for the XX spectrum is then based on string fragments.…”

Section: Introductionmentioning

confidence: 99%

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Quasiparticles in the XXZ model

Lu¹,

Müller²,

Karbach³

2009

Condens. Matter Phys.

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The coordinate Bethe ansatz solutions of the XXZ model for a one-dimensional spin-1/2 chain are analyzed with focus on the statistical properties of the constituent quasiparticles. Emphasis is given to the special cases known as XX, XXX, and Ising models, where considerable simplifications occur. The XXZ spectrum can be generated from separate pseudovacua as configurations of sets of quasiparticles with different exclusion statistics. These sets are complementary in the sense that the pseudovacuum of one set contains the maximum number of particles from the other set. The Bethe ansatz string solutions of the XXX model evolve differently in the planar and axial regimes. In the Ising limit they become ferromagnetic domains with integer-valued exclusion statistics. In the XX limit they brake apart into hard-core bosons with (effectively) fermionic statistics. Two sets of quasiparticles with spin 1/2 and fractional statistics are distinguished, where one set (spinons) generates the XXZ spectrum from the unique, critical ground state realized in the planar regime, and the other set (solitons) generates the same spectrum from the twofold, antiferromagnetically ordered ground state realized in the axial regime. In the Ising limit, the solitons become antiferromagnetic domain walls.

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Section: Limit: Broken Strings Fermions and Spinonsmentioning

confidence: 83%

“…The second term in (13) ensures that the set {I i } remains the same as an eigenstate is tracked across the axial regime [7]. Here x is the floor function (integer part of x).…”

Section: Axial Regimementioning

confidence: 99%

Section: Limit: Strings and Spinonsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quasiparticles in the XXZ model

Lu¹,

Müller²,

Karbach³

2009

Condens. Matter Phys.

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“…Another consequence is that the advances recently reported in the calculation of transition rates via algebraic Bethe ansatz for the XXZ model [19] can be translated into corresponding advances, for ∆ → 0, in the fermion representation of the XX model [17].…”

Section: Magnons and Fermionsmentioning

confidence: 99%

Interaction and thermodynamics of spinons in theXXchain

Karbach

Müller

Wiele

2008

J. Phys. A: Math. Theor.

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Abstract. The mapping between the fermion and spinon compositions of eigenstates in the one-dimensional spin-1/2 XX model on a lattice with N sites is used to describe the spinon interaction from two different perspectives: (i) For finite N the energy of all eigenstates is expressed as a function of spinon momenta and spinon spins, which, in turn, are solutions of a set of Bethe ansatz equations. The latter are the basis of an exact thermodynamic analysis in the spinon representation of the XX model. (ii) For N → ∞ the energy per site of spinon configurations involving any number of spinon orbitals is expressed as a function of reduced variables representing momentum, filling, and magnetization of each orbital. The spins of spinons in a single orbital are found to be coupled in a manner well described by an Ising-like equivalent-neighbor interaction, switching from ferromagnetic to antiferromagnetic as the filling exceeds a critical level. Comparisons are made with results for the Haldane-Shastry model.

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Spinon excitations in the spin-1 XXZ chain and hidden supersymmetry

Matsui

2016

Nuclear Physics B

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We study spinon excitations of the integrable spin-1 (Fateev-Zamolodchikov; FZ) chain and their relation to the hidden supersymmetry. Using the notion of the supercharges earlier introduced to the spin chains, which change the system length by one, we found that they nontrivially act on one of two kinds of the degrees of freedom for the FZ chain. Their actions were obtained to be the same as those of the supercharges defined on the supersymmetric sine-Gordon model, the low-energy effective field theory of the FZ chain. Moreover, we construct the eigenstates which are invariant under the supersymmetric Hamiltonian given as the anti-commutator of the supercharges.

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Spinon excitations in theXXchain: spectra, transition rates, observability

Cited by 18 publications

References 22 publications

Quasiparticles in the XXZ model

Quasiparticles in the XXZ model

Interaction and thermodynamics of spinons in theXXchain

Spinon excitations in the spin-1 XXZ chain and hidden supersymmetry

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