Abstract
We study dynamical properties at finite temperature of Heisenberg spin chains with random antiferromagnetic exchange couplings, which realize the random singlet phase in the low-energy limit, using three complementary numerical methods: exact diagonalization, matrix-product-state algorithms, and stochastic analytic continuation of quantum Monte Carlo results in imaginary time. Specifically, we investigate the dynamic spin structure factor and its limit, which are closely related to inelastic neutron scattering and nuclear magnetic resonance (NMR) experiments (through the spin-lattice relaxation rate . Our study reveals a continuous narrow band of low-energy excitations in , extending throughout the space, instead of being restricted to and as found in the uniform system. Close to , the scaling properties of these excitations are well captured by the random-singlet theory, but disagreements also exist with some aspects of the predicted dependence further away from . Furthermore we also find spin diffusion effects close to that are not contained within the random-singlet theory but give non-negligible contributions to the mean . To compare with NMR experiments, we consider the distribution of the local relaxation rates . We show that the local values are broadly distributed, approximately according to a stretched exponential. The mean first decreases with , but below a crossover temperature it starts to increase and likely diverges in the limit of a small nuclear resonance frequency . Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean has never been experimentally observed. Indeed, we show that the divergence of the mean is due to rare events in the disordered chains and is concealed in experiments, where the typical value is accessed.
7 More- Received 6 December 2017
- Revised 26 February 2018
DOI:https://doi.org/10.1103/PhysRevB.97.104424
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