Deformed strings in the Heisenberg model

Abstract

We investigate solutions to the Bethe equations for the isotropic S = 1/2 Heisenberg chain involving complex, string-like rapidity configurations of arbitrary length. Going beyond the traditional string hypothesis of undeformed strings, we describe a general procedure to construct eigenstates including strings with generic deformations, discuss general features of these solutions, and provide a number of explicit examples including complete solutions for all wavefunctions of short chains. We finally investigate some singular cases and show from simple symmetry arguments that their contribution to zero-temperature correlation functions vanishes.

34 pages, 13 figures

References in corpus (11)

• Computation of dynamical correlation functions of Heisenberg chains in a field
• Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
• The 4-spinon dynamical structure factor of the Heisenberg chain
• Bethe's equation is incomplete for the XXZ model at roots of unity
• Introduction to the Bethe ansatz II
• Violation of the string hypothesis and Heisenberg XXZ spin chain
• Completeness of Bethe's states for generalized $XXZ$ model
• Large N behavior of string solutions in the Heisenberg model
• Violations of the String Hypothesis in the Solutions of the Bethe Ansatz Equations in the XXX-Heisenberg
• Completeness of ``Good'' Bethe Ansatz Solutions of a Quantum Group Invariant Heisenberg Model
• Origin of the singular Bethe ansatz solutions for the Heisenberg XXZ spin chain

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