Landau-Lifschitz magnets: exact thermodynamics and transport
arXiv:2404.12106 · doi:10.1103/PhysRevLett.133.107102
Abstract
The classical Landau--Lifshitz equation -- the simplest model of a ferromagnet -- provides an archetypal example for studying transport phenomena. In one-spatial dimension, integrability enables the classification of the spectrum of linear and nonlinear modes. An exact characterization of finite-temperature thermodynamics and transport has nonetheless remained elusive. We present an exact description of thermodynamic equilibrium states in terms of interacting modes. This is achieved by retrieving the classical Landau--Lifschitz model through the semiclassical limit of the integrable quantum spin- anisotropic Heisenberg chain at the level of the thermodynamic Bethe ansatz description. In the axial regime, the mode spectrum comprises solitons with unconventional statistics, whereas in the planar regime we additionally find two special types of modes of radiative and solitonic type. The obtained framework paves the way for analytical study of unconventional transport properties: as an example we study the finite-temperature spin Drude weight, finding excellent agreement with Monte Carlo simulations.
4 pages, 2 figures
References in corpus (28)
- Many-Body Physics with Ultracold Gases
- Experimental Observation of a Generalized Gibbs Ensemble
- Spin transport in a one-dimensional anisotropic Heisenberg model
- Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
- Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
- Transport in out-of-equilibrium XXZ chains: non-ballistic behavior and correlation functions
- Superdiffusion in spin chains
- Correlation functions and transport coefficients in generalised hydrodynamics
- Generalized Hydrodynamics in the 1D Bose gas: theory and experiments
- Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
- Kardar-Parisi-Zhang universality from soft gauge modes
- Universal relaxational dynamics of gapped one dimensional models in the quantum sine-Gordon universality class
- Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
- Ballistic macroscopic fluctuation theory
- Absence of Normal Fluctuations in an Integrable Magnet
- Emergence of hydrodynamic spatial long-range correlations in nonequilibrium many-body systems
- Emergent Pauli blocking in a weakly interacting Bose gas
- Distinct universality classes of diffusive transport from full counting statistics
- Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
- Kinetic theory of quantum and classical Toda lattices
- Dynamical criticality of magnetization transfer in integrable spin chains
- Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
- Exact Thermodynamics and Transport in the Classical Sine-Gordon Model
- The sine-Gordon model from coupled condensates: a Generalized Hydrodynamics viewpoint
- Hydrodynamic equations for the Ablowitz-Ladik discretization of the nonlinear Schroedinger equation
- Anisotropic Landau-Lifshitz Model in Discrete Space-Time
- New classical integrable systems from generalized -deformations
- Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission