Dynamical properties of the S=1/2 random Heisenberg chain

Yu-Rong Shu (1, 2) , Maxime Dupont (3, 4) , Dao-Xin Yao (1) , Sylvain Capponi (3, 4) , Anders W Sandvik (2)

1 SYSU - Sun Yat-sen University [Guangzhou]
2 Department of Physics [Boston]
3 FFC - Fermions Fortement Corrélés (LPT)
4 LPT - Laboratoire de Physique Théorique

We study dynamical properties at finite temperature (T) of Heisenberg spin chains with random anti-ferromagnetic 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/T 1). 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/T 1. To compare with NMR experiments, we consider the distribution of the local relaxation rates 1/T 1. We show that the local 1/T 1 values are broadly distributed, approximately according to a stretched exponential. The mean 1/T 1 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 ω 0. Although a similar divergent behavior has been predicted and experimentally observed for the static uniform susceptibility, this divergent behavior of the mean 1/T 1 has never been experimentally observed. Indeed, we show that the divergence of the mean 1/T 1 is due to rare events in the disordered chains and is concealed in experiments, where the typical 1/T 1 value is accessed.

Domaines: Electrons fortement corrélés [cond-mat.str-el]

Yu-Rong Shu, Maxime Dupont, Dao-Xin Yao, Sylvain Capponi, Anders W Sandvik. Dynamical properties of the S=1/2 random Heisenberg chain. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2018, 97 (10), pp.104424. ⟨10.1103/PhysRevB.97.104424⟩. ⟨hal-01774900⟩