Form factors of the XXZ Heisenberg finite chain

Kitanine, N.; Maillet, Jean Michel; Terras, V.

doi:10.1016/s0550-3213(99)00295-3

Cited by 447 publications

(938 citation statements)

References 41 publications

(85 reference statements)

Supporting

Mentioning

911

Contrasting

Unclassified

Order By: Relevance

“…A proof of these results together with their extension to non-zero magnetic field has been obtained in 1999 [14,15] for both regimes using algebraic Bethe ansatz [16,17] and the actual resolution of the so-called quantum inverse scattering problem [14,18].…”

Section: Introductionmentioning

confidence: 92%

“…To compute these elementary blocks, the following successive problems have to be addressed [14,15]: (i) determination of the ground state ψ g |, (ii) evaluation of the action of the product of the local operators E j , j j on this ground state, and (iii) computation of the scalar product of the resulting state with |ψ g .…”

Section: Introductionmentioning

confidence: 99%

“…For the XXZ spin-1 2 Heisenberg chain in a magnetic field, these problems have been solved in [14,15] in the framework of algebraic Bethe ansatz. The central object of this method is the so called quantum monodromy matrix depending on a complex variable λ (the spectral parameter).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Spin–spin correlation functions of the XXZ- Heisenberg chain in a magnetic field

et al. 2002

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spin–spin correlation functions of the XXZ- Heisenberg chain in a magnetic field

et al. 2002

Self Cite

View full text Add to dashboard Cite

show abstract

“…(5) for significantly large chains. Unfortunately, unlike the Heisenberg model, there are so far no determinant formulas 45 or vertex operator approach 46 to compute form factors for the Hubbard model. Nonetheless, we can use the BA equations to compute the exact support of the DSF.…”

Section: Elementary Excitations In the Bethe Ansatz Solutionmentioning

confidence: 99%

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

et al. 2012

View full text Add to dashboard Cite

We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U → ∞ and a subset of the two-holontwo-spinon continuum that reconstructs the electron-hole continuum in the limit U → 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and η-spin SU (2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U = 0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a Van Hove singularity that persists as a consequence of integrability.

show abstract

“…In [3], the Drinfeld twists associated with any finite-dimensional irreducible representations of the Yangian Y [gl (2)] were investigated. In [4], the form factors for local spin operators of the spin-1/2 XXZ model were computed and in [5], the spontaneous magnetization of the XXZ chain on the finite lattice was represented. In [2], Albert et al constructed the F -matrix of the gl(m) rational Heisenberg model and obtained a polarization free representation of the creation operators.…”

Section: Introductionmentioning

confidence: 99%

Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetrict-JModel

Yang

Zhang

Zhao

2004

J. High Energy Phys.

View full text Add to dashboard Cite

We construct the Drinfeld twists (factorizing F -matrices) for the supersymmetric t-J model. Working in the basis provided by the F -matrix (i.e. the so-called F -basis), we obtain completely symmetric representations of the monodromy matrix and the pseudo-particle creation operators of the model. These enable us to resolve the hierarchy of the nested Bethe vectors for the gl(2|1) invariant t-J model. I IntroductionThe algebraic Bethe ansatz or the quantum inverse scattering method (QISM) provides a powerful tool of solving eigenvalue problems such as diagonalizing integrable two-dimensional quantum spin chains. In this framework, the pseudo-particle creation and annihilation operators are constructed by the off-diagonal entries of the monodromy matrix. The Bethe vectors (eigenvectors) are obtained by acting the creation operators on the pseudo-vacuum state. However, the apparently simple action of creation operators is intricate on the level of the local operators by non-local effects arising from polarization clouds or compensating exchange terms. This makes the exact and explicit computation of correlation functions difficult (if not impossible).Recently, Maillet and Sanchez de Santos [1] showed how monodromy matrices of the inhomogeneous XXX and XXZ spin chains can be simplified by using the factorizing Drinfeld twists. This leads to the natural F -basis for the analysis of these models. In this basis, the pseudo-particle creation and annihilation operators take completely symmetric forms and contain no compensating exchange terms on the level of the local operators (i.e. polarization free). As a result, the Bethe vectors of the models are simplified dramatically and can be written down explicitly.The results of [1] were generalized to certain other systems. In [3], the Drinfeld twists associated with any finite-dimensional irreducible representations of the Yangian Y [gl(2)] were investigated. In [4], the form factors for local spin operators of the spin-1/2 XXZ model were computed and in [5], the spontaneous magnetization of the XXZ chain on the finite lattice was represented. In [2], Albert et al constructed the F -matrix of the gl(m) rational Heisenberg model and obtained a polarization free representation of the creation operators. Using these results, they resolved the hierarchy of the nested

show abstract

Form factors of the XXZ Heisenberg finite chain

Cited by 447 publications

References 41 publications

Spin–spin correlation functions of the XXZ- Heisenberg chain in a magnetic field

Spin–spin correlation functions of the XXZ- Heisenberg chain in a magnetic field

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

Drinfeld Twists and Algebraic Bethe Ansatz of the Supersymmetrict-JModel

Contact Info

Product

Resources

About