Nonlocal effects of low-energy excitations in quantum-spin-liquid candidate Cu$_3$Zn(OH)$_6$FBr

TL;DR

This study investigates the low-temperature specific heat behavior of a kagome antiferromagnet, revealing nonlocal quantum effects and excitations consistent with a $Z_2$ quantum spin liquid, providing insights into topological order.

Contribution

The paper presents large-scale quantum Monte Carlo simulations linking specific heat features to gapped anyons and impurities in a $Z_2$ quantum spin liquid model, highlighting nonlocal quantum effects.

Findings

Specific heat follows a $T^{1.7}$ dependence at low temperatures.

The shoulder feature's entropy decreases with grain size, indicating nonlocal effects.

The coherence length of quantum entangled excitations is comparable to superconducting coherence lengths.

Abstract

We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet, Cu$_{3}$Zn(OH)$_6$FBr. The specific heat exhibits a $T^{1.7}$ dependence at low temperatures and a shoulder-like feature above it. We construct a microscopic lattice model of $Z_2$ quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities. Surprisingly, we find the entropy associated with the shoulder decreases quickly with grain size $d$, although the system is paramagnetic to the lowest temperature. While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface, the 5.9-nm shell width precludes any trivial explanations. Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate, similar to Pippard's coherence length in superconductors. Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.