We use recent developments in the framework of a time-dependent matrix product state method to compute the nuclear magnetic resonance relaxation rate 1/T 1 for spin-1/2 chains under magnetic field and for different Hamiltonians (XXX, XXZ, isotropically dimerized). We compute numerically the temperature dependence of the 1/T 1 . We consider both gapped and gapless phases, and also the proximity of quantum critical points. At temperatures much lower than the typical exchange energy scale, our results are in excellent agreement with analytical results, such as the ones derived from the Tomonaga-Luttinger liquid (TLL) theory and bosonization, which are valid in this regime. We also cover the regime for which the temperature T is comparable to the exchange coupling. In this case analytical theories are not appropriate, but this regime is relevant for various new compounds with exchange couplings in the range of tens of Kelvin. For the gapped phases, either the fully polarized phase for spin chains or the low-magnetic-field phase for the dimerized systems, we find an exponential decrease in /(k B T ) of the relaxation time and can compute the gap . Close to the quantum critical point our results are in good agreement with the scaling behavior based on the existence of free excitations.

We present measurements of the magnetic entropy landscape and Grüneisen parameter of the Cu2+ complex (C5 H12 N)2 CuCl4 in a magnetic field. Our thermodynamic measurements are in very good agreement with a theoretical description by a S = 1/2 Heisenberg ladder model. Due to its excellent experimental access, the compound crosses two quantum critical points in the applied range of the magnetic field, first from a gapped unpolarized state to a critical phase and then to a gapped fully polarized state. This behavior is reflected directly in the magnetic entropy map. Due to the remarkable properties of the magnetic Gru ̈neisen parameter, we are able to discuss the validity of critical behavior with respect to temperature and magnetic field for this model quasi-one-dimensional system

We present a comparison between the bosonization results for quantum quenches and exact diagonalizations in microscopic models of interacting spinless fermions in a one-dimensional lattice. The numerical analysis of the long-time averages shows that density-density correlations at small momenta tend to a non-zero limit, mimicking a thermal behavior. These results are at variance with the bosonization approach, which predicts the presence of long-wavelength critical properties in the long-time evolution.By contrast, the numerical results for finite momenta suggest that the singularities at 2kF in the densitydensity correlations and at kF in the momentum distribution are preserved during the time evolution.The presence of an interaction term that breaks integrability flattens out all singularities, suggesting that the time evolution of one-dimensional lattice models after a quantum quench may differ from that of the Luttinger model.

We use the density matrix renormalization group method (DMRG) to compute the frequency and momentum resolved spin-spin correlation functions of a dimerized spin-1/2 chain under a magnetic field at finite temperature. The spectral features strongly depend on the regime of the magnetic field. For increasing magnetic fields, the transitions from a gapped spin liquid phase to a Tomonaga-Luttinger liquid, and then to a totally polarized phase, can be identified in the spectra. Compared to the zero temperature case, the finite temperature excitations give rise to additional spectral features that we compute numerically and identify analytically as transitions from thermally excited states. We compute quantitatively the broadening of the dispersion of a single spin-flip excitation due to the temperature and find a strong asymmetric broadening. We discuss the consequences of these findings for neutron experiments on dimerized one dimensional quantum chains. arXiv:1710.07811v2 [cond-mat.str-el]