Static and dynamical spin correlations of the S=1/2 random-bond antiferromagnetic Heisenberg model on the triangular and the kagome lattices

TL;DR

This study investigates the static and dynamical spin correlations in the S=1/2 random-bond antiferromagnetic Heisenberg model on triangular and kagome lattices, providing insights into the nature of quantum spin liquids and their experimental signatures.

Contribution

It offers the first detailed analysis of spin correlations in the randomness-induced quantum spin liquid state using exact diagonalization, linking theoretical models to experimental observations.

Findings

Weak wavevector dependence of $S(q,)$ in the random-singlet state

Gapless behaviors with broad energy distribution in spin correlations

Almost flat dynamical structure factor in the kagome model

Abstract

Inspired by the recent theoretical suggestion that the random-bond $S=1/2$ antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin liquid (QSL) behavior when the strength of the randomness exceeds a critical value, and that this "random-singlet state" might be relevant to the QSL behaviors experimentally observed in triangular organic salts $\kappa {\rm -(ET)_2 Cu_2 (CN)_3}$and ${\rm EtMe_3 Sb[Pd(dmit)_2]_2}$ and in kagome herbertsmithite ${\rm CuZn_3(OH)_6Cl_2}$, we further investigate the nature of the static and the dynamical spin correlations of these models. We compute the static and the dynamical spin structure factors, $S({\bf q})$ and $S({\bf q},\omega)$, by means of an exact diagonalization method. In both triangular and kagome models, the computed $S({\bf q},\omega)$ in the random-singlet state depends on the wavevector ${\bf q}$ only weakly, robustly exhibiting gapless behaviors accompnied by the broad distribution extending to higher energy $\omega$. Especially in the strongly random kagome model, $S({\bf q},\omega)$ hardly depends on ${\bf q}$, and exhibits an almost flat distribution for a wide range of $\omega$, together with a $\omega=0$ peak. These features agree semi-quantitatively with the recent neutron-scattering data on a single-crystal herbertsmithite, suggesting that the QSL state observed in herbersmithite might indeed be the randomness-induced QSL state, {\it i.e.\/}, the random-singlet state.