Dynamical properties of the S=1/2 random Heisenberg chain
Sandvik, Anders W.
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Citation (published version)Yu-Rong Shu, Maxime Dupont, Dao-Xin Yao, Sylvain Capponi, Anders W Sandvik. 2018. "Dynamical properties of the S=1/2 random Heisenberg chain." Physical Review B, Volume 97, Issue 10. https://doi.org/10.1103/PhysRevB.97.104424
We study dynamical properties at finite temperature (T) 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 S(q,ω) and its ω→0 limit, which are closely related to inelastic neutron scattering and nuclear magnetic resonance (NMR) experiments (through the spin-lattice relaxation rate 1/T1). Our study reveals a continuous narrow band of low-energy excitations in S(q,ω), extending throughout the q space, instead of being restricted to q≈0 and q≈π as found in the uniform system. Close to q=π, the scaling properties of these excitations are well captured by the random-singlet theory, but disagreements also exist with some aspects of the predicted q dependence further away from q=π. Furthermore we also find spin diffusion effects close to q=0 that are not contained within the random-singlet theory but give non-negligible contributions to the mean 1/T1. To compare with NMR experiments, we consider the distribution of the local relaxation rates 1/T1. We show that the local 1/T1 values are broadly distributed, approximately according to a stretched exponential. The mean 1/T1 first decreases with T, but below a crossover temperature it starts to increase and likely diverges in the limit of a small nuclear resonance frequency ω0. Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean 1/T1 has never been experimentally observed. Indeed, we show that the divergence of the mean 1/T1 is due to rare events in the disordered chains and is concealed in experiments, where the typical 1/T1 value is accessed.