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:0710.5904 · Journal of Statistical Mechanics Theory and Experiment

The thermodynamical limit of generalgl(N) spin chains: II. Excited states and energies

Nicolas Crampé, L. Frappat, E. Ragoucy

Published Jan 18, 2008• 2 citations
arXivHTMLPDF

Abstract

We consider the thermodynamical limit of a gl ( N ) spin chain with arbitrary representation at each site of the chain. We study the first excitations (with holes and new strings) above the vacuum and compute the corresponding densities of the Bethe roots as well as their energy.
DOI
10.1088/1742-5468/2008/01/p01015

Related papers

Thermodynamical limit of general gl(N) spin chains II: Excited states and energies

Nicolas Crampé, L. Frappat, E. Ragoucy

We consider the thermodynamical limit of a gl(N) spin chain with arbitrary representation at each site of the chain. We consider excitations (with holes and new strings) above the vacuum and compute their corrections in 1/L to the densities and the energy.

•Jan 1, 2008•0 citations

The thermodynamical limit of generalgl(N) spin chains: the vacuum state and densities

Nicolas Crampé, L. Frappat, E. Ragoucy

We study the vacuum state of spin chains where each site carries an arbitrary representation. We prove that the string hypothesis usually used to solve the Bethe ansatz equations is valid for representations characterized by rectangular Young tableaux. In these cases, we obtain the density of the centre of the strings for the vacuum. We work through different examples and, in particular, that for spin chains with a periodic array of impurities.

arXiv:cond-mat/0701207•Journal of Statistical Mechanics Theory and Experiment•Mar 28, 2007•4 citations

Thermodynamical limit of general gl(N) spin chains: vacuum state and densities

Nicolas Crampé, L. Frappat, E. Ragoucy

We study the vacuum state of spin chains where each site carry an arbitrary representation. We prove that the string hypothesis, usually used to solve the Bethe ansatz equations, is valid for representations characterized by rectangular Young tableaux. In these cases, we obtain the density of the center of the strings for the vacuum. We work out different examples and, in particular, the spin chains with periodic array of impurities.

•Jan 1, 2005•0 citations

Analytic continuation of Bethe energies and application to the thermodynamic limit of the SL(2, ℂ) non-compact spin chains

Etienne Granet, Jesper Lykke Jacobsen, Hubert Saleur

A bstract We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one can expand the analytic continuation of energies in the scaling limit around another ‘pseudo-vacuum’ sitting at a negative number of Bethe roots, in the same way as around the usual pseudo-vacuum. We show that this method can be used to compute the energy levels of some states of the SL(2, ℂ) integrable spin chain in the infinite-volume limit, and as a proof of principle recover the ground-state value previously obtained in [1] (for the case of spins s = 0 , $$ \overline{s} $$ s ¯ = − 1) by extrapolating results in small sizes. These results represent, as far as we know, the first (partial) description of the spectrum of SL(2, ℂ) non-compact spin chains in the thermodynamic limit.

arXiv:2005.06030•Journal of High Energy Physics•Aug 1, 2020•3 citations

Excitations and theS-matrix for ansu(3)spin chain combining and representations

J Abad, M Ríos

The associated Hamiltonian for an su (3) spin chain combining and representations is calculated. The ansatz equations for this chain are obtained and solved in the thermodynamic limit, and the ground state and excitations are described. Thus, relations between the number of roots and the number of holes in each level have been found. The excited states are characterized by means of these quantum numbers. Finally, the exact S -matrix for a state with two holes is found.

arXiv:cond-mat/9801129•Journal of Physics A Mathematical and General•Mar 13, 1998•0 citations

Excitations and S-matrix for su(3) spin chain combining {3} and {3 ∗ } representations

J. Abad, M. Ríos

The associated Hamiltonian for a su(3) spin chain combining {3} and {3 ∗ } representations is calculated. The ansatz equations for this chain are obtained and solved in the thermodynamic limit, and the ground state and excitations are described. Thus, relations between the number of roots and the number of holes in each level have been found. The excited states are characterized by means of these quantum numbers. Finally, the exact S matrix for a state with two holes is found. PACS

•Jan 1, 1998•2 citations
A bstract We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one can expand the analytic continuation of energies in the scaling limit around another ‘pseudo-vacuum’ sitting at a negative number of Bethe roots, in the same way as around the usual pseudo-vacuum. We show that this method can be used to compute the energy levels of some states of the SL(2, ℂ) integrable spin chain in the infinite-volume limit, and as a proof of principle recover the ground-state value previously obtained in [1] (for the case of spins s = 0 , s‾ \overline{s} s s ¯ = − 1) by extrapolating results in small sizes. These results represent, as far as we know, the first (partial) description of the spectrum of SL(2, ℂ) non-compact spin chains in the thermodynamic limit.