Spin spin correlation functions of the XXZ - 1/2 Heisenberg chain in a magnetic field

By N. Kitanine, J. Maillet, N. Slavnov, V. Terras. 2002

171 citations recorded by the source corpus.

Abstract Using algebraic Bethe ansatz and the solution of the quantum inverse scattering problem, we compute compact representations of the spin–spin correlation functions of the XXZ- 1 2 Heisenberg chain in a magnetic field. At lattice distance m, they are typically given as the sum of m terms. Each term n of this sum, n=1,…,m, is represented in the thermodynamic limit as a multiple integral of order 2n+1; the integrand depends on the distance as the power m of some simple function. The root of these results is the derivation of a compact formula for the multiple action on a general quantum state of the chain of transfer matrix operators for arbitrary values of their spectral parameters.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/408dd16e55222c8218b8c09531dd4702e0482947

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. V. Alba
2. Pasquale Calabrese
3. M. Fagotti
4. J. Cardy
5. E. Tonni
6. F. Essler
7. T. Takayanagi
8. T. Nishioka

In Condensed Matter Physics

1. V. Alba
2. M. Fagotti
3. Pasquale Calabrese
4. J. Cardy
5. E. Tonni
6. T. Takayanagi
7. T. Nishioka
8. Thomas Hartman

In Geometry and Topology

1. Pasquale Calabrese
2. V. Alba
3. M. Fagotti
4. J. Cardy

Citations in the corpus

• Integral representations for correlation functions of the XXZ chain at finite temperature (2004, methodology): “In addition, efficient formulae for norms [11], scalar product s [15], and the multiple action of certain non-local operators [5] are available for th e generalized model [11] defined by theR-matrix of the XXZ chain.”
• Entanglement entropy of excited states (2009, background): “Some further advances for the algebraic Bethe ansatz approach to the XXZ model can be found in [34].”
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions (2008, methodology): “The starting point of our approach is an exact expression, that we called the master equation representation, for the generating function of the two-point correlation functions of these models that we obtained in our previous works [48, 50, 51, 45].”