Dynamical structure factor of random antiferromagnetic Heisenberg spin chains

TL;DR

This study uses quantum Monte Carlo and maximum entropy methods to analyze how bond randomness affects the dynamical structure factor in spin-1/2 antiferromagnetic Heisenberg chains, revealing a crossover from spinon excitations to broad disorder-induced features.

Contribution

It provides detailed numerical analysis of the dynamical structure factor across different disorder regimes, highlighting the crossover from pure to disorder-dominated phases in antiferromagnetic chains.

Findings

Broad non-spinon excitations at the infinite randomness fixed point.

Clear spinon signatures in weak disorder regimes.

Implications for experimental observations in real materials.

Abstract

Combining quantum Monte Carlo simulations with the maximum entropy method, we study the dynamical structure factor $S(k,\omega)$ of spin-1/2 antiferromagnetic Heisenberg chains with various random bond distributions. We emphasize the crossover behavior in the dynamical properties from pure chain to disorder-dominated random singlet phase due to bond randomness. For the distribution corresponding to the infinite randomness fixed point, $S(k,\omega)$ develops broad non-spinon excitations as well as the random-singlet peak near $(k, \omega) = (\pi, 0)$, consistent with the known results obtained by the real-space renormalization group method. For weak disorder, however, we find clear signature of spinon excitations, reminiscent of pure spin chains, blurred by disorder. We discuss the implication for experiments on random-bond antiferromagnetic spin chains, realizable, e.g., in BaCu$_2$(Si$_x$Ge$_{1-x}$)$_2$O$_7$.