Transition rates via Bethe ansatz for the spin-1/2 planar<i>XXZ</i>antiferromagnet

Biegel, Daniel; Karbach, Michael; Müller, Gerhard

doi:10.1088/0305-4470/36/20/301

Cited by 28 publications

(43 citation statements)

References 21 publications

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“…Although the determinants cannot be computed explicitly, they can be evaluated numerically by solving the underlying Bethe Ansatz equations on a computer. This approach turned out to be efficient for the calculation of experimentally relevant correlation functions [7,11,38,39].…”

Section: Introductionmentioning

confidence: 99%

Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime

Dugave¹,

Göhmann²,

Kozłowski³

et al. 2016

J. Phys. A: Math. Theor.

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We use the form factors of the quantum transfer matrix in the zero-temperature limit in order to study the two-point ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime. We obtain novel form factor series representations of the correlation functions which differ from those derived either from the q-vertex-operator approach or from the algebraic Bethe Ansatz approach to the usual transfer matrix. We advocate that our novel representations are numerically more efficient and allow for a straightforward calculation of the large-distance asymptotic behaviour of the two-point functions. Keeping control over the temperature corrections to the two-point functions we see that these are of order T ∞ in the whole antiferromagnetic massive regime. The isotropic limit of our result yields a novel form factor series representation for the two-point correlation functions of the XXX chain at zero magnetic field. *

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Section: Introductionmentioning

confidence: 99%

Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime

Dugave¹,

Göhmann²,

Kozłowski³

et al. 2016

J. Phys. A: Math. Theor.

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“…Our purpose will be to compute the contribution to this quantity coming from all two-spinon intermediate states, using two separate methods relying on integrability. The first method applies to finite lattices, and makes use of determinant expressions for spin operator form factors derived within the Algebraic Bethe Ansatz [12,13] and used to compute structure factors of Heisenberg chains for general fields and anisotropies, both for two-particle [14,15,16] and general multiparticle states [17,18]. The second method starts from an algebraic analysis of the infinite chain in zero field [19], and uses the quantum group symmetry of the model to express states and form factors directly in the thermodynamic limit.…”

Section: Introductionmentioning

confidence: 99%

The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain

Caux¹,

Mossel²,

Castillo³

2008

J. Stat. Mech.

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Abstract. We consider the transverse dynamical structure factor of the anisotropic Heisenberg spin-1/2 chain (XXZ model) in the gapped antiferromagnetic regime (∆ > 1). Specializing to the case of zero field, we use two independent approaches based on integrability (one valid for finite size, the other for the infinite lattice) to obtain the exact two-spinon part of this correlator. We discuss in particular its asymmetry with respect to the π/2 momentum line, its overall anisotropy dependence, and its contribution to sum rules.The two-spinon transverse structure factor of the gapped Heisenberg AFM chain 2

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“…Also expanding the prefactor in Eq. (32) and rearranging the expressions by taking a common factor out of the matrix elements we obtain…”

Section: The Long Wavelength Limitmentioning

confidence: 99%

Nature of the many-body excitations in a quantum wire: Theory and experiment

et al. 2016

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The natural excitations of an interacting one-dimensional system at low energy are hydrodynamic modes of Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where quadratic dispersion reduces the symmetry to Galilean, the main character of the many-body excitations changes into a hierarchy: calculations of dynamic correlation functions for fermions (without spin) show that the spectral weights of the excitations are proportional to powers of R 2 /L 2 , where R is a length-scale related to interactions and L is the system length. Thus only small numbers of excitations carry the principal spectral power in representative regions on the energy-momentum planes. We have analysed the spectral function in detail and have shown that the first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalised single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power-laws at the spectral edge. We have illustrated crossover to Luttinger liquid at low energy by calculating the local density of state through all energy scales: from linear to non-linear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure momentum-resolved tunnelling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe well-resolved spin-charge separation at low energy with appreciable interaction strength and only a parabolic dispersion of the first-level mode at higher energies. We find structure resembling the second-level excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.

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Transition rates via Bethe ansatz for the spin-1/2 planarXXZantiferromagnet

Cited by 28 publications

References 21 publications

Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime

Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime

The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain

Nature of the many-body excitations in a quantum wire: Theory and experiment

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