5 research outputs found
How to calculate correlation functions of Heisenberg chains
We describe a method for calculating dynamical spin-spin correlation
functions in the finite isotropic and anisotropic antiferromagnetic Heisenberg
models. Our method is able to produce results with high accuracy over the full
parameter space.Comment: Proceedings of the "Tenth Training Course in the Physics of
Correlated Electron Systems and High-Tc Superconductors", Salerno, Oct 200
Gapped Heisenberg spin chains in a field
We consider the fully anisotropic Heisenberg spin-1/2 antiferromagnet in a
uniform magnetic field, whose ground-state is characterized by broken spin
rotation symmetry and gapped spinon excitations. We expand on a recent
mean-field approach to the problem by incorporating fluctuations in a loop
expansion. Quantitative results for the magnetization, excitation gap and
specific heat are obtained. We compare our predictions with new DMRG and exact
diagonalization data and, for zero field, with the exact solution of the
spin chain from the Bethe Ansatz.Comment: 11 pages, 14 figure
Deformed strings in the Heisenberg model
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.Comment: 34 pages, 13 figure
Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime
We compute all dynamical spin-spin correlation functions for the spin-1/2
anisotropic Heisenberg model in the gapless antiferromagnetic regime,
using numerical sums of exact determinant representations for form factors of
spin operators on the lattice. Contributions from intermediate states
containing many particles and string (bound) states are included. We present
modified determinant representations for the form factors valid in the general
case with string solutions to the Bethe equations. Our results are such that
the available sum rules are saturated to high precision. We Fourier transform
our results back to real space, allowing us in particular to make a comparison
with known exact formulas for equal-time correlation functions for small
separations in zero field, and with predictions for the zero-field asymptotics
from conformal field theory.Comment: 14 page