Statistically interacting quasiparticles in Ising chains

Lu, Ping; Vanasse, Jared; Piecuch, Christopher G.; Karbach, Michael; Müller, Gerhard

doi:10.1088/1751-8113/41/26/265003

Cited by 19 publications

(49 citation statements)

References 27 publications

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“…All domains have the same energy, J. The statistical mechanics of domains for the Ising chain has been carried out exactly [26], reproducing familiar results. In the context of figure 2 we have already qualitatively described the antiferromagnetic domain walls (solitons) that are complementary to the ferromagnetic domains.…”

Section: Ising Limit: Stretched Strings Domains and Solitonsmentioning

confidence: 77%

“…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%

“…They can be tracked all the way from ∆ → ∞ to ∆ = 0. A comparison between the spinon composition and soliton composition of the XX eigenstates can be found in [26].…”

Section: Limit: Broken Strings Fermions and Spinonsmentioning

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: Ising Limit: Stretched Strings Domains and Solitonsmentioning

confidence: 77%

Section: Limit: Strings and Spinonsmentioning

confidence: 99%

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Quasiparticles in the XXZ model

Lu¹,

Müller²,

Karbach³

2009

Condens. Matter Phys.

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“…The results presented here for the XX limit (∆ = 0) set the stage for one point from which to attack this challenge. A natural second point of attack is the Ising limit (∆ = ∞), where the mapping between top-down quasiparticles (ferromagnetic domains) and bottom-up quasiparticles (antiferromagnetic domain walls) is again transparent and where the latter are again spin-1/2 particles with semionic statistics [22].…”

Section: Discussionmentioning

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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“…6, are again associated with the combined limit (20). Equation (26) for w 2 remains valid if we divide the left-hand side by (1 + R f ) 2 .…”

Section: Frictionmentioning

confidence: 99%

Jammed disks in a narrow channel: criticality and ordering tendencies

Gundlach¹,

Karbach²,

Liú³

et al. 2013

J. Stat. Mech.

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Abstract. A system of identical disks is confined to a narrow channel, closed off at one end by a stopper and at the other end by a piston. All surfaces are hard and frictionless. A uniform gravitational field is directed parallel to the plane of the disks and perpendicular to the axis of the channel. We employ a method of configurational statistics that interprets jammed states as configurations of floating particles with structure. The particles interlink according to set rules. The two jammed microstates with smallest volume act as pseudo-vacuum. The placement of particles is subject to a generalized Pauli principle. Jammed macrostates are generated by random agitations and specified by two control variables. They are inferred from measures for expansion work against the piston, gravitational potential energy, and intensity of random agitations. In this two-dimensional space of variables there exists a critical point. The jammed macrostate realized at the critical point depends on the path of approach. We describe all jammed macrostates by volume and entropy. Both are functions of the average population densities of particles. Approaching the critical point in an extended space of control variables generates two types of jammed macrostates: states with random heterogeneities in mass density and states with domains of uniform mass density. Criticality is shown to be robust against some effects of friction.

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Statistically interacting quasiparticles in Ising chains

Cited by 19 publications

References 27 publications

Quasiparticles in the XXZ model

Quasiparticles in the XXZ model

Interaction and thermodynamics of spinons in theXXchain

Jammed disks in a narrow channel: criticality and ordering tendencies

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