Dynamical properties of the S=12 random Heisenberg chain

Abstract

We study dynamical properties at finite temperature (T ) of Heisenberg spin chains with random antiferrormagnetic 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. *

Spin excitation spectra of the two-dimensional S=12 Heisenberg model with a checkerboard structure

“…The SAC method we use here is the standard form that uses a parametrization of the spectral function with a large number of equal-amplitude δ functions [19,20]. The inverse of the Laplace transform in Eq.…”

“…Since S (q, ω) can be accessed directly by INS and nuclear magnetic resonance (NMR) experiments, the most favorable evidence for the validity of the QMC-SAC method is that the calculated S (q, ω) results are in good agreement with the existing experimental results [19]. As an effective numerical method for calculating the complete spectra, the QMC-SAC method has recently been used in some interesting work, such as the spin excitation spectrum of the random singlet state [20], quantum spin liquids [13], the dynamical signature of fractionalization at a deconfined quantum critical point [12], and the dynamics of the Higgs mode in spin systems [21,22]. However, unlike the results given by analytical studies, the effects of various modes of spin excitation are intermingled in the results obtained with QMC-SAC.…”

From order to randomness: Onset and evolution of the random-singlet state in bond-disordered BaCu2(Si1−xGex)2Shiroka1, Eggenschwiler2, Ott3 et al. 2019Phys. Rev. B10150View full textAdd to dashboardCite

“…What exactly happens when a regular spinchain is exposed to an increasing degree of disorder is not well known. Until recently, progress has been slow as far as numerical simulations 13 and, especially, experimental investigations [14][15][16] of disordered low-dimensional systems are concerned. The main reasons include computational difficulties due to the large size of realistic disordered systems and, regarding experiments, the scarcity of suitable systems in which disorder can be easily tuned over a broad range without changing the structural character of the material.…”

The correlation functions of certain random antiferromagnetic spin-1∕2 critical chains

“…For uncorrelated disorder, we have proposed and numerically verified that the correlations in Eqs. (7), (10), (16) are good approximations in the regime γ D r ≫ 1 (not restricted to the thermodynamic limit r ≪ L) for periodic boundary conditions. We have shown that the chord length (8) is not the true scaling variable exhibiting small corrections for the mean correlations and even smaller for the typical ones.…”

“…The reason is that for smaller values of D, the slope A α is not fully saturated (due to the effects of the crossover 7 We consider only the data such that C xx typ < 2.5 10 −2 and C zz typ < 2.0 10 −4 . This is simply to ensure some meaning to the fitting function (16) when disorder is weak (D < 0.6). As we explain latter on, this has no influence in our results.…”