NMR relaxation rate in quasi-one-dimensional antiferromagnets

Quasi-one-dimensional antiferromagnets are good candidates to realize a Tomonaga-Luttinger liquid (TLL), describing 1D interacting quantum systems, provided 3D coupling remains small as compared to temperature. In such systems, made of weakly coupled spin chains, interchain coupling plays an important role at low temperature as it leads to a spontaneous symmetry breaking below the critical temperature. Using time-dependent numerical simulations at finite temperature [1] we have computed and studied the NMR relaxation rate in S=1/2 antiferromagnetic XXZ spin chains to address the question of the low-temperature crossover between TLL predictions and the higher-temperature regime. To understand the effect of the three-dimensional coupling on the NMR relaxation rate (close to and at the transition), we analyze the full 3D microscopic model using quantum Monte-Carlo techniques. This allows to compute dynamical correlations in imaginary time and we will discuss recent advances to perform stochastic analytic continuation to get real frequency spectra that can be compared to analytical self-consistent approximations results [2].

[1] M. Dupont, S. Capponi, N. Laflorencie, Phys. Rev. B 94, 144409 (2016)
[2] M. Dupont, S. Capponi, N. Laflorencie, E. Orignac, in preparation