| The low-energy properties of critical one-dimensional quantum systems are usually well described by the Luttinger model. Recent studies, however, have shown that this is not true for the long-time dynamics. At zero temperature the long-time behavior of correlation functions can instead be dominated by high-energy excitations which are connected to edge singularities in the dynamical structure factor. Another violation of the Luttinger liquid paradigm can occur at finite temperatures where Umklapp scattering can be a dangerously irrelevant perturbation leading to a new low-energy contribution which dominates the long-time behavior of correlation functions. Concentrating on the anisotropic Heisenberg model, I will discuss consequences of these findings for quantities such as the spin structure factor, the spin-lattice relaxation rate, and transport. |
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