Lattice vs. continuum theory of the periodic Heisenberg chain

Abstract

We consider the detailed structure of low energy excitations in the periodic spin-1/2 XXZ Heisenberg chain. By performing a perturbative calculation of the non-linear corrections to the Gaussian model, we determine the exact coefficients of asymptotic expansions in inverse powers of the system length N for a large number of low-lying excited energy levels. This allows us to calculate eigenenergies of the lattice model up to order order N^-4, without having to solve the Bethe Ansatz equations. At the same time, it is possible to express the exact eigenstates of the lattice model in terms of bosonic modes.

17 pages, 8 Figures. The latest version can be found at http://www.physik.uni-kl.de/eggert/papers/index.html

References in corpus (7)

• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Exact dynamics in the inhomogeneous central-spin model
• Quantum quenches from integrability: the fermionic pairing model
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Deformed strings in the Heisenberg model
• Local Density of States for Individual Energy Levels in Finite Quantum Wires
• Spinon excitations in the XX chain: spectra, transition rates, observability

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• Sine-square deformation of solvable spin chains and conformal field theories
• The even-odd effect in short antiferromagnetic Heisenberg chains
• Unconventional Neel and dimer orders in a spin-1/2 frustrated ferromagnetic chain with easy-plane anisotropy
• Recursive Method for the Density of States in One Dimension
• Ground-state phase diagram of a spin-1/2 frustrated XXZ ladder
• Fine structure of the nonlinear Drude weights in the spin-1/2 XXZ chain
• The dynamic structure factor in impurity-doped spin chains