Temperature dependence of the NMR spin-lattice relaxation rate for spin-12chains

Abstract

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.

NMR relaxation in the spin-1 Heisenberg chain

“…Let us also point out that, since the spin gap is field dependent, the finite magnetic field needs to be taken into account for a quantitative analysis [26,27,62,63]. In some other related systems, such as an explicit dimerized S = 1/2 chain (which is also a one-dimensional gapped system), it has been shown for instance that a simple activated law 1/T 1 ∝ exp(−β∆) holds [17,64] for the NMR relaxation rate. It will be interesting to investigate other simple, yet non trivial, gapped one-dimensional systems such as spin-1/2 ladder or other dimerized chains where a simple activated law is often measured [65][66][67][68][69][70][71].…”

Finite-temperature correlations in a quantum spin chain near saturation

“…[34,36] Table I. For each different value, the T-DMRG converged to a thermal equilibrium distribution e −βH/2 easily.…”

“…For some simple cases, the development of theses DMRG-based tools has allowed to extract equilibrium correlations at finite temperatures (T-DMRG) [32,33]. This provided a welcome guidance to experiments [34][35][36] especially in situations where temperature is too high for a brute force application of field theory.…”

Low-dimensional correlations under thermal fluctuations

“…We also compare the direct numerical calculations with the field theory description at finite temperature in order to have a feeling of the range of validity of the field theory description, in a spirit similar to what was done previously for NMR. 33 The plan of the paper is as follows. In Sec.…”