Dynamic correlation functions for one-dimensional quantum-spin systems: New results based on a rigorous approach
- 1 January 1984
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 29 (1), 288-301
- https://doi.org/10.1103/physrevb.29.288
Abstract
We present new results on the time-dependent correlation functions , , at zero temperature of the one-dimensional isotropic model () and of the transverse Ising (TI) model at the critical magnetic field (). Both models are characterized by special cases of the Hamiltonian . We have derived exact results on the long-time asymptotic expansions of the autocorrelation functions and on the singularities of their frequency-dependent Fourier transforms . We have also determined the latter functions by high-precision numerical calculations. The functions , , have singularities at the infinite sequence of frequencies , , where for the model and for the TI model. In the TI case, the leading singularities in are alternately one-sided and two-sided power-law singularities, the first two of which (at ) are divergent. The dominant singularities in the case are alternate one-sided power laws and two-sided power laws with logarithmic corrections, the first two of which (at ) are divergent. The singularities at higher frequencies in both models are finite and become increasingly weaker. We point out that the nonanalyticities at are intrinsic features of the discrete quantum chain and have therefore not been found in the context of a continuum analysis (Luttinger model). At least the most prominent features of our new results should be observable in low-temperature dynamical experiments on quasi-one-dimensional compounds such as the -like substances Co
Keywords
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