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On Bethe Vectors for the XXZ Model at Roots of Unity

V. Tarasov

Journal of Mathematical SciencesDec 4, 20049 citations

Bethe's Equation Is Incomplete for the XXZ Model at Roots of Unity

Klaus Fabricius, Barry M. McCoy

arXiv:cond-mat/0009279Journal of Statistical PhysicsJun 1, 200193 citations

Solutions of the Bethe Equations for the XXZ Model

V. Tarasov

Journal of Mathematical SciencesDec 4, 20040 citations

An analytic treatment of finite-size corrections in the spin-1 antiferromagnetic XXZ chain

Andreas Klümper, Murray T. Batchelor

It is known that the standard method for calculating finite-size corrections in Bethe ansatz solvable systems is not applicable to the Takhtajan-Babujian model and its anisotropic XXZ generalisation. The authors develop a new analytic method explicitly avoiding root densities and associated problems. Nonlinear integral equations are derived whose solutions yield the correct central charges c=1 and c=3/2 for the spin-1/2 and spin-1 XXZ chains, respectively. In the spin-1 case the authors obtain as a by-product the finite-size deviation of the Bethe ansatz roots from the 2-string formation.It is known that the standard method for calculating finite-size corrections in Bethe ansatz solvable systems is not applicable to the Takhtajan-Babujian model and its anisotropic XXZ generalisation. The authors develop a new analytic method explicitly avoiding root densities and associated problems. Nonlinear integral equations are derived whose solutions yield the correct central charges c=1 and c=3/2 for the spin-1/2 and spin-1 XXZ chains, respectively. In the spin-1 case the authors obtain as a by-product the finite-size deviation of the Bethe ansatz roots from the 2-string formation.

Journal of Physics A Mathematical and GeneralMar 7, 199091 citations

Root patterns and energy spectra of quantum integrable systems without U(1) symmetry: the antiperiodic XXZ spin chain

Xiong Le, Yi Qiao, Junpeng Cao +3 more

Abstract Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without U(1) symmetry, their spectra are usually given by inhomogeneous T − Q relations and the Bethe root patterns are still unclear. In this paper with the antiperiodic XXZ spin chain as an example, an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit is proposed. Based on them the ground state energy and elementary excitations in the gapped regime are derived. The present method provides an universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit.Abstract Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without U(1) symmetry, their spectra are usually given by inhomogeneous T − Q relations and the Bethe root patterns are still unclear. In this paper with the antiperiodic XXZ spin chain as an example, an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit is proposed. Based on them the ground state energy and elementary excitations in the gapped regime are derived. The present method provides an universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit.

arXiv:2108.08060Journal of High Energy PhysicsNov 1, 20219 citations

Functional Relations and Bethe Ansatz for the XXZ Chain

Rafael I. Nepomechie

arXiv:hep-th/0211001Journal of Statistical PhysicsApr 7, 2003148 citations

On Condensation Properties of Bethe Roots Associated with the XXZ Chain

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