Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain

TL;DR

This paper provides experimental evidence that the spin dynamics in a quantum Heisenberg antiferromagnetic chain follow the Kardar-Parisi-Zhang universality class, revealing emergent quantum fluid behavior through neutron scattering.

Contribution

It demonstrates that neutron scattering can detect KPZ universality in quantum spin chains, linking quantum hydrodynamics to classical statistical physics.

Findings

Spin dynamics exhibit a dynamical exponent z=3/2.

Evidence supports KPZ universality class in quantum spin chain.

Neutron scattering reveals emergent quantum fluid properties.

Abstract

Classical hydrodynamics is a remarkably versatile description of the coarse-grained behavior of many-particle systems once local equilibrium has been established. The form of the hydrodynamical equations is determined primarily by the conserved quantities present in a system. Some quantum spin chains are known to possess, even in the simplest cases, a greatly expanded set of conservation laws, and recent work suggests that these laws strongly modify collective spin dynamics even at high temperature. Here, by probing the dynamical exponent of the one-dimensional Heisenberg antiferromagnet KCuF$_3$ with neutron scattering, we find evidence that the spin dynamics are well described by the dynamical exponent $z=3/2$, which is consistent with the recent theoretical conjecture that the dynamics of this quantum system are described by the Kardar-Parisi-Zhang universality class. This observation shows that low-energy inelastic neutron scattering at moderate temperatures can reveal the details of emergent quantum fluid properties like those arising in non-Fermi liquids in higher dimensions.