Nonlinear Fluctuating Hydrodynamics for the Classical XXZ Spin Chain

Abstract

Using the framework of nonlinear fluctuating hydrodynamics (NFH), we examine equilibrium spatio-temporal correlations in classical ferromagnetic spin chains with nearest neighbor interactions. In particular, we consider the classical XXZ-Heisenberg spin chain (also known as Lattice Landau Lifshitz or LLL model) evolving deterministically and chaotically via Hamiltonian dynamics, for which energy and $z$-magnetization are the only locally conserved fields. For the easy-plane case, this system has a low-temperature regime in which the difference between neighboring spin's angular orientations in the XY plane is an \textit{almost conserved} field. According to the predictions of NFH, the dynamic correlations in this regime exhibit a heat peak and propagating sound peaks, all with anomalous broadening. We present a detailed molecular dynamics test of these predictions and find a reasonably accurate verification. We find that, in a suitable intermediate temperature regime, the system shows two sound peaks with Kardar-Parisi-Zhang (KPZ) scaling and a heat peak where the expected anomalous broadening is less clear. In high temperature regimes of both easy plane and easy axis case of LLL, our numerics show clear diffusive spin and energy peaks and absence of any sound modes, as one would expect. We also simulate an integrable version of the XXZ-model, for which the ballistic component instead moves with a broad range of speeds rather than being concentrated in narrower peaks around the sound speed.

arXiv comment32 pages, 16 figures

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• Classical many-body chaos with and without quasiparticles
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• Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
• Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
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• The 1+1 dimensional Kardar-Parisi-Zhang equation: more surprises
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• Anomalous current fluctuations from Euler hydrodynamics
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• Exact Solution for the Heat Conductance in Harmonic Chains
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• Dynamical regimes of finite temperature discrete nonlinear Schrödinger chain
• Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
• Particle Scattering and Fusion for the Ablowitz-Ladik Chain
• Diagnosing quantum transport from wave function snapshots
• Thermalization and Hydrodynamics of Two-Dimensional Quantum Field Theories
• Superdiffusion resilience in Heisenberg Chains with 2D interactions on a quantum processor
• Lindblad quantum dynamics from correlation functions of classical spin chains
• Soliton-like behaviour in non-integrable systems
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