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Spin diffusion from an inhomogeneous quench in an integrable system.

Marko Ljubotina1, Marko Žnidarič1, Tomaž Prosen1

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Statistical Mechanics

Background:

  • Integrable lattice systems typically exhibit ballistic transport in generic inhomogeneous states, as predicted by generalized hydrodynamics.
  • Discrete symmetries can alter transport properties, potentially leading to non-ballistic behavior.
  • The anisotropic Heisenberg XXZ spin 1/2 chain is a key model for studying quantum transport phenomena.

Purpose of the Study:

  • To investigate spin transport in the anisotropic Heisenberg XXZ spin 1/2 chain under specific symmetric initial conditions.
  • To determine whether ballistic transport is suppressed and to characterize the nature of non-ballistic transport.
  • To analyze the scaling behavior of magnetization and spin density profiles in different regimes.

Main Methods:

  • Large-scale numerical simulations of spin dynamics.
  • Preparation of an inhomogeneous mixed initial state symmetric under spin reversal and spatial reflection.
  • Analysis of scaling exponents for transported magnetization and scaling profiles of spin density.

Main Results:

  • Non-ballistic spin transport was observed in both isotropic and easy-axis regimes.
  • Accurate evidence of normal diffusion was found in the easy-axis regime.
  • In the isotropic case, super-diffusive spin transport with a scaling exponent near 2/3 was identified, exhibiting universal dynamics governed by a diffusion equation in nonlinearly scaled time.

Conclusions:

  • The presence of specific discrete symmetries breaks the universal ballistic transport predicted by generalized hydrodynamics in integrable systems.
  • Spin transport in the anisotropic Heisenberg XXZ chain can transition from normal diffusion to super-diffusion depending on the system's parameters and initial state.
  • The observed super-diffusive transport in the isotropic regime suggests novel scaling dynamics beyond simple diffusion.