Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0612348 · Journal of Physics A Mathematical and Theoretical

String correlation functions of the spin-1/2 HeisenbergXXZchain

Michael Bortz, Jun Sato, Masahiro Shiroishi

Published Mar 30, 2007• 15 citations
arXivHTMLPDF

Abstract

We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain exact results from Bethe Ansatz and exact diagonalization, whereas in the large-distance limit, field-theoretical arguments yield an asymptotic algebraic decay. We also make contact with two-point spin-correlation functions in the asymptotic limit.

DOI
10.1088/1751-8113/40/16/001

Related papers

Correlation functions of the higher spinXXXchains

N Kitanine

Using the algebraic Bethe ansatz, we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin ½ Heisenberg chain, based on the solution of the quantum inverse problem. We construct a representation for the correlation functions on a finite chain for arbitrary spin. Then we show how the string solutions of the Bethe equations can be considered in the framework of this approach in the thermodynamic limit. Finally, a multiple integral representation for the spin 1 zero-temperature correlation functions is obtained in the thermodynamic limit.

arXiv:math-ph/0104016•Journal of Physics A Mathematical and General•Sep 21, 2001•41 citations

CORRELATION FUNCTIONS OF THE XXZ SPIN-½ HEISENBERG CHAIN: RECENT ADVANCES (REVIEW)

N Kitanine, Jean Michel Maillet, N. A. Slavnov +1 more

We review some recent advances in the computation of exact correlation functions of the XXZ-½ Heisenberg chain. We first give a general introduction to our method which is based on the algebraic Bethe ansatz and the resolution of the quantum inverse scattering problem, leading in particular to multiple integral representations for the correlation functions. Then we describe recently obtained compact formulas for the spin-spin correlation functions of the XXZ-½ Heisenberg chain. We outline how this leads to several explicit results including the known two point functions in the limit of free fermions, the so-called emptiness formation probability at anisotropy Δ=1/2 and its large distance asymptotic behaviour in the massless phase of the model.

International Journal of Modern Physics A•May 1, 2004•5 citations

Correlation functions of the XXZ Heisenberg spin chain: Bethe ansatz approach

Jean Michel Maillet

We review recent progress in the computation of correlation functions of the XXZ spin-1/2 chain. We describe both finite and infinite chain results. Long distance asymptotic behavior is discussed. Our method is based on the resolution of the quantum inverse scattering problem in the framework of the algebraic Bethe ansatz.

Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006•May 15, 2007•1 citation

String correlation functions in the anisotropic spin-1 Heisenberg chain

Francisco Castilho Alcaraz, Yasuhiro Hatsugai

We study the string correlation functions proposed by den Nijs and Rommelse for the S=1 XXZ Hamiltonian by an exact diagonalization method. Using a finite size analysis, we estimate values of the string order parameters in the thermodynamic limit. Using the extrapolated values of the string order parameter we investigate the phase boundary between the two expected phases of the model, namely, the massive Haldane phase and the x-y--like massless phase. In the massless phase the exponent of the string correlation functions on the periodic system seems to be given by dimensions, which normally occur in the operator content of the chain when antiperiodic boundary condition is imposed.

Physical review. B, Condensed matter•Dec 1, 1992•34 citations

Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime

Jean-Sébastien Caux, Rob Hagemans, Jean Michel Maillet

We compute all dynamical spin–spin correlation functions for the spin-1/2 XXZ anisotropic Heisenberg model in the gapless antiferromagnetic regime at zero temperature, using numerical sums of exact determinant representations for form factors of spin operators on the lattice. Contributions from intermediate states containing many particles and string (bound) states are included. We present modified determinant representations for the form factors valid in the general case with string solutions to the Bethe equations. Our results are such that the available sum rules are saturated to high precision. We Fourier transform our results back to real space, allowing us in particular to make a comparison with known exact formulae for equal-time correlation functions for small separations in zero field, and with predictions for the zero-field asymptotics from conformal field theory.

arXiv:cond-mat/0506698•Journal of Statistical Mechanics Theory and Experiment•Sep 1, 2005•148 citations

Exact Calculation of Correlation Functions for Spin-1/2 Heisenberg Chain

Masahiro Shiroishi, Minoru Takahashi

We review the recent progresses of the exact calculation of the correlation functions for the spin-1/2 Heisenberg XXX chain as well as the anisotropic XXZ chain. The spin-1/2 Heisenberg chain is exactly solvable by Bethe ansatz. Nevertheless the exact calculation of the correlation functions is still a very difficult problem in general. However, the recent theoretical developments have enabled us to derive the explicit analytical forms of some correlation functions in short range. For example, polynomial representations in terms of the one-dimensional integrals are obtained for the correlation functions of the XXZ chain up to four lattice sites. For the special case of the XXX chain, the correlation functions are further calculated up to five lattice sites.

Journal of the Physical Society of Japan•Jan 1, 2005•17 citations
We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain exact results from Bethe Ansatz and exact diagonalization, whereas in the large-distance limit, field-theoretical arguments yield an asymptotic algebraic decay. We also make contact with two-point spin-correlation functions in the asymptotic limit.
Using the algebraic Bethe ansatz, we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin ½ Heisenberg chain, based on the solution of the quantum inverse problem. We construct a representation for the correlation functions on a finite chain for arbitrary spin. Then we show how the string solutions of the Bethe equations can be considered in the framework of this approach in the thermodynamic limit. Finally, a multiple integral representation for the spin 1 zero-temperature correlation functions is obtained in the thermodynamic limit.
We review some recent advances in the computation of exact correlation functions of the XXZ-½ Heisenberg chain. We first give a general introduction to our method which is based on the algebraic Bethe ansatz and the resolution of the quantum inverse scattering problem, leading in particular to multiple integral representations for the correlation functions. Then we describe recently obtained compact formulas for the spin-spin correlation functions of the XXZ-½ Heisenberg chain. We outline how this leads to several explicit results including the known two point functions in the limit of free fermions, the so-called emptiness formation probability at anisotropy Δ=1/2 and its large distance asymptotic behaviour in the massless phase of the model.
We study the string correlation functions proposed by den Nijs and Rommelse for the S=1 XXZ Hamiltonian by an exact diagonalization method. Using a finite size analysis, we estimate values of the string order parameters in the thermodynamic limit. Using the extrapolated values of the string order parameter we investigate the phase boundary between the two expected phases of the model, namely, the massive Haldane phase and the x-y--like massless phase. In the massless phase the exponent of the string correlation functions on the periodic system seems to be given by dimensions, which normally occur in the operator content of the chain when antiperiodic boundary condition is imposed.
We compute all dynamical spin–spin correlation functions for the spin-1/2 XXZ anisotropic Heisenberg model in the gapless antiferromagnetic regime at zero temperature, using numerical sums of exact determinant representations for form factors of spin operators on the lattice. Contributions from intermediate states containing many particles and string (bound) states are included. We present modified determinant representations for the form factors valid in the general case with string solutions to the Bethe equations. Our results are such that the available sum rules are saturated to high precision. We Fourier transform our results back to real space, allowing us in particular to make a comparison with known exact formulae for equal-time correlation functions for small separations in zero field, and with predictions for the zero-field asymptotics from conformal field theory.
We review the recent progresses of the exact calculation of the correlation functions for the spin-1/2 Heisenberg XXX chain as well as the anisotropic XXZ chain. The spin-1/2 Heisenberg chain is exactly solvable by Bethe ansatz. Nevertheless the exact calculation of the correlation functions is still a very difficult problem in general. However, the recent theoretical developments have enabled us to derive the explicit analytical forms of some correlation functions in short range. For example, polynomial representations in terms of the one-dimensional integrals are obtained for the correlation functions of the XXZ chain up to four lattice sites. For the special case of the XXX chain, the correlation functions are further calculated up to five lattice sites.