Dynamical dimer-dimer correlation functions from exact diagonalization

Abstract

Preprint. Typeset using REVT E XA regularization method is presented to deduce dynamic correlation functions from exact diagonalization calculations. It is applied to dimer-dimer correlation functions in quantum spin chains relevant for the description of spin-Peierls systems. Exact results for the XY model are presented. The analysis draws into doubt that the dimer-dimer correlation functions show the same scale invariance as spin-spin correlation functions. The results are applied to describe the quasi-elastic scattering in CuGeO3.

Lineshapes of dynamical correlation functions in Heisenberg chains

“…To determine the correlation functions in frequency space we use the same methods as described in Ref. 17 which we briefly summarize. At low temperatures small systems exhibit a small number of dominant spectral lines at frequenciesω j which usually can be attributed to specific excitations.…”

“…(6) gives very accurate results for the real part of the correlation function if it is determined at the dominant spectral linesω j . 17 Re…”

“…(16)) as well as the decay in real time space as given by Eq. (17). The upper continuum edge Λ positions the cusp or divergence of the real part (Eq.…”

“…The crucial point is that Re χ(q, ω → ∞) depends only weakly on the system size L. 17 Figure 3(c) shows I 1 (q, T ) as a function of temperature for different system sizes and frustration parameters. In Fig.…”

“…In the case of finite systems it proves thus useful to actually calculate all three representations to extrapolate to the thermodynamic limit. 17 The dynamical correlation functions become system size independent for high excitation energies 17 or, equivalently, on short time scales. 4 While finite systems thus allow for the determination of correlation functions in the thermodynamic limit at high frequencies or on short time scales, field theoretical results describe their asymptotic behavior on long time scales or for small frequencies.…”