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arXiv:2009.13535 · Nature Physics

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

A. Scheie, Nicholas E. Sherman, Maxime Dupont, S. E. Nagler, M. B. Stone, G. E. Granroth, Joel E. Moore, D. A. Tennant

Published Mar 11, 2021• 129 citations
arXivHTMLPDF
DOI
10.1038/s41567-021-01191-6

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Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable spin chains have time-reversal and parity symmetries that are absent from the KPZ (Kardar-Parisi-Zhang) or stochastic Burgers equation, which force higher-order spin fluctuations to deviate from standard KPZ predictions. We put forward a nonlinear fluctuating hydrodynamic theory consisting of two coupled stochastic modes: the local spin magnetization and its effective velocity. Our theory fully explains the emergence of anomalous spin dynamics in isotropic chains: it predicts KPZ scaling for the spin structure factor but with a symmetric, quasi-Gaussian, distribution of spin fluctuations. We substantiate our results using matrix-product states calculations.
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.
Recent investigations have observed superdiffusion in integrable classical and quantum spin chains. An intriguing connection between these spin chains and the Kardar-Parisi-Zhang (KPZ) universality class has emerged. Theoretical developments (e.g., generalized hydrodynamics) have highlighted the role of integrability as well as spin symmetry in KPZ behavior. However, understanding their precise role on superdiffusive transport still remains a challenging task. The widely used quantum spin chain platform comes with severe numerical limitations. To circumvent this barrier, we focus on a classical integrable spin chain which was shown to have a deep analogy with the quantum spin-12\frac{1}{2}21​ Heisenberg chain. Remarkably, we find that KPZ behavior prevails even when one considers integrability-breaking but spin-symmetry preserving terms, strongly indicating that spin symmetry plays a central role even in the nonperturbative regime. On the other hand, in the nonperturbative regime, we find that energy correlations exhibit clear diffusive behavior. We also study the classical analog of the out-of-time-ordered correlator and Lyapunov exponents. We find a significant presence of chaos for the integrability-broken cases even though KPZ behavior remains robust. The robustness of KPZ behavior is demonstrated for a wide class of spin-symmetry preserving integrability-breaking terms.