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


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.

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Fig. 1: One-dimensional physics in KCuF3.
Fig. 2: Measured neutron spectrum of KCuF3.
Fig. 3: Power-law behaviour of KCuF3 around Q = 0.
Fig. 4: Temperature evolution of the KCuF3 neutron spectra around Q = 0.

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All plotted experimental data are publicly available at


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This manuscript has been authored by UT-Batelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide licence to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( N.E.S., M.D. and J.E.M. were supported by the DOE, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract no. DE-AC02-05-CH11231 through the Scientific Discovery through Advanced Computing (SciDAC) programme (KC23DAC Topological and Correlated Matter via Tensor Networks and Quantum Monte Carlo). During the last period of the work, N.E.S. was supported by the DOE, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract no. DE-AC02-05-CH11231 through the Theory Institute for Molecular Spectroscopy (TIMES). J.E.M. was also supported by a Simons Investigatorship. This research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. D.A.T. and J.E.M. were supported by the DOE, Office of Science, National Quantum Information Science Research Centers. This research also used the Lawrencium computational cluster resource provided by the IT Division at the Lawrence Berkeley National Laboratory (supported by the Director, Office of Science, Office of Basic Energy Sciences, of the DOE under contract no. DE-AC02-05-CH11231). This research used resources of the Compute and Data Environment for Science (CADES) at the Oak Ridge National Laboratory, which is supported by the Office of Science of the DOE under contract no. DE-AC05-00OR22725. This research also used resources of the National Energy Research Scientific Computing Center (NERSC), a US Department of Energy Office of Science User Facility operated under contract no. DE-AC02-05CH11231.

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The project was conceived by J.E.M. and D.A.T. The experiments were performed by A.S., M.B.S., S.E.N. and D.A.T. The numerical simulations and theoretical analysis were performed by N.E.S., M.D. and J.E.M. The neutron data analysis was performed by A.S. with input from D.A.T., G.E.G. and S.E.N. The results were discussed and the paper written by A.S., N.E.S., M.D., S.E.N., J.E.M. and D.A.T.

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Correspondence to J. E. Moore or D. A. Tennant.

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Peer review information Nature Physics thanks Andrew Boothroyd, Igor Zaliznyak and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Scheie, A., Sherman, N.E., Dupont, M. et al. Detection of Kardar–Parisi–Zhang hydrodynamics in a quantum Heisenberg spin-1/2 chain. Nat. Phys. 17, 726–730 (2021).

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