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Bulletin of the American Physical Society

Detection of Kardar-Parisi-Zhang Hydrodynamics in a quantum Heisenberg spin-half chain

Nicholas E. Sherman, Allen O. Scheie, Maxime Dupont, S. E. Nagler, M. B. Stone, Garrett E. Granroth, Joel E. Moore, D. M. Tennant

Published Mar 16, 2021• 0 citations
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Classical hydrodynamics is a remarkably versatile description of the coarse-grained behaviour of many-particle systems once local equilibrium has been established1. 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 temperature2,3. Here, by probing the dynamical exponent of the one-dimensional Heisenberg antiferromagnet KCuF3 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 class4,5. 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.
The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of a wealth of classical stochastic models. Surprisingly, KPZ universality was recently conjectured to also describe spin transport in the one-dimensional quantum Heisenberg model. We tested this conjecture by experimentally probing transport in a cold-atom quantum simulator via the relaxation of domain walls in spin chains of up to 50 spins. We found that domain-wall relaxation is indeed governed by the KPZ dynamical exponent z = 3/2 and that the occurrence of KPZ scaling requires both integrability and a nonabelian SU(2) symmetry. Finally, we leveraged the single-spin–sensitive detection enabled by the quantum gas microscope to measure an observable based on spin-transport statistics. Our results yield a clear signature of the nonlinearity that is a hallmark of KPZ universality.