Inelastic neutron-scattering and finite-temperature density matrix renormalization group (DMRG) calculations are used to investigate the spin excitation spectrum of the S = 1/2 Heisenberg spin chain compound K 2 CuSO 4 Cl 2 at several temperatures in a magnetic field near saturation. Critical correlations characteristic of the predicted z = 2, d = 1 quantum phase transition occurring at saturation are shown to be consistent with the observed neutron spectra. The data is well described with a scaling function computed using a free fermion description of the spins, valid close to saturation, and the corresponding scaling limits. One of the most prominent nonuniversal spectral features of the data is a novel thermally activated longitudinal mode that remains underdamped across most of the Brillouin zone.

We study the correlation functions of quantum spin 1/2 two-leg ladders at finite temperature, under a magnetic field, in the gapless phase at various relevant temperatures T = 0, momenta q, and frequencies ω. We compute those quantities using the time-dependent density-matrix renormalization group (T-DMRG) in an optimal numerical scheme. We compare these correlations with the ones of dimerized quantum spin chains and simple spin chains, that we compute by a similar technique. We analyze the intermediate energy modes and show that the effect of temperature leads to the formation of an essentially dispersive mode corresponding to the propagation of a triplet mode in an incoherent background, with a dispersion quite different from the one occurring at very low temperatures. We compare the low-energy part of the spectrum with the predictions of the Tomonaga-Luttinger liquid field theory at finite temperature. We show that the field theory describes in a remarkably robust way the low-energy correlations for frequencies or temperatures up to the natural cutoff (the effective dispersion) of the system. We discuss how our results could be tested in, e.g., neutron-scattering experiments. arXiv:1901.04339v2 [cond-mat.str-el]

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