Abstract
Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. However, the ballistic contribution to transport can vanish in systems with additional discrete symmetries. Here we perform large scale numerical simulations of spin dynamics in the anisotropic Heisenberg XXZ spin 1/2 chain starting from an inhomogeneous mixed initial state which is symmetric with respect to a combination of spin reversal and spatial reflection. In the isotropic and easy-axis regimes we find non-ballistic spin transport which we analyse in detail in terms of scaling exponents of the transported magnetization and scaling profiles of the spin density. While in the easy-axis regime we find accurate evidence of normal diffusion, the spin transport in the isotropic case is clearly super-diffusive, with the scaling exponent very close to 2/3, but with universal scaling dynamics which obeys the diffusion equation in nonlinearly scaled time.
Highlights
Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states
A naive classical reasoning might be that, because integrable systems are distinguished by constants of motion that force the dynamics to be simple and almost periodic, one should expect to see ballistic transport
A generalization of hydrodynamics has been put forward[8,9] which successfully predicts ballistic currents and scaled density profiles of integrable interacting systems quenched from inhomogeneous initial states[10,11,12,13,14,15], which is a convenient method to study relaxation and non-equilibrium transport
Summary
Generalized hydrodynamics predicts universal ballistic transport in integrable lattice systems when prepared in generic inhomogeneous initial states. While in the easy-axis regime we find accurate evidence of normal diffusion, the spin transport in the isotropic case is clearly super-diffusive, with the scaling exponent very close to 2/3, but with universal scaling dynamics which obeys the diffusion equation in nonlinearly scaled time Integrable models, such as the classical Kepler problem, harmonic oscillators, the planar Ising problem and so on, form cornerstones of our understanding of nature. In extended interacting integrable system a macroscopic number of local conservation laws exists, in number proportional to the number of degrees of freedom, which can be exploited to develop generalized hydrodynamics[8] This theory for typical inhomogeneous initial states predicts ballistic scaling f(x 1⁄4 x/t) of densities and currents of conserved quantities, such as energy, charge or magnetization. This means that the transported conserved quantity at x 1⁄4 0 grows slower than linear with t
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