Dynamical properties of the S=12 random Heisenberg chain

Yu-Rong Shu, Maxime Dupont, Dao-Xin Yao, Sylvain Capponi, and Anders W. Sandvik
Phys. Rev. B 97, 104424 – Published 28 March 2018

Abstract

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 ω0 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 q0 and qπ 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.

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  • Received 6 December 2017
  • Revised 26 February 2018

DOI:https://doi.org/10.1103/PhysRevB.97.104424

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Yu-Rong Shu1,2, Maxime Dupont2,3, Dao-Xin Yao1,*, Sylvain Capponi2,3,†, and Anders W. Sandvik2,‡

  • 1State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
  • 2Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
  • 3Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, F-31062 Toulouse, France

  • *yaodaox@mail.sysu.edu.cn
  • capponi@irsamc.ups-tlse.fr
  • sandvik@bu.edu

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Issue

Vol. 97, Iss. 10 — 1 March 2018

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