期刊
PHYSICAL REVIEW B
卷 97, 期 10, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.97.104424
关键词
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资金
- GENCI [x2016050225, x2017050225]
- Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund [NKRDPC-2017YFA0206203, NSFC-11574404, NSFC-11275279, NSFG-2015A030313176]
- Leading Talent Program of Guangdong Special Projects
- French ANR program BOLODISS [ANR-14-CE32-0018]
- Region Midi-Pyrenees
- Condensed Matter Theory Visitors Program at Boston University
- NEXT [ANR-11-IDEX-0002-02, ANR-10-LABX-0037]
- NSF [DMR-1710170]
- Simons Foundation
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, omega) and its omega -> 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, omega), extending throughout the q space, instead of being restricted to q approximate to 0 and q approximate to pi as found in the uniform system. Close to q = pi, 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 = pi. 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 omega(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.
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