Absence of superdiffusion in certain random spin models

Abstract

The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain was found to be superdiffusive in numerous recent numerical and experimental studies. Theoretical approaches to this problem have emphasized the role of nonabelian SU(2) symmetry as well as integrability but the associated methods cannot be readily applied when integrability is broken. We examine spin transport in a spin-1/2 chain in which the exchange couplings fluctuate in space and time around a nonzero mean $J$, a model introduced by De Nardis et al. [Phys. Rev. Lett. 127, 057201 (2021)]. We show that operator dynamics in the strong noise limit at infinite temperature can be analyzed using conventional perturbation theory as an expansion in $J$. We find that regular diffusion persists at long times, albeit with an enhanced diffusion constant. The finite time spin dynamics is analyzed and compared with matrix product operator simulations.

4+3 pages

References in corpus (7)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Superdiffusion in spin chains
• Ballistic spin transport in a periodically driven integrable quantum system
• Stability of superdiffusion in nearly integrable spin chains
• Correlations and commuting transfer matrices in integrable unitary circuits

Cited by in corpus (14)

• Anomalous transport from hot quasiparticles in interacting spin chains
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
• Superdiffusion from nonabelian symmetries in nearly integrable systems
• Real-time correlators in chaotic quantum many-body systems
• Corrections to diffusion in interacting quantum systems
• Slow crossover from superdiffusion to diffusion in isotropic spin chains
• A Bound on Thermalization from Diffusive Fluctuations
• Superdiffusive magnetization transport in the XX spin chain with non-local dephasing
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Superdiffusive transport on lattices with nodal impurities
• Noise Induced Universal Diffusive Transport in Fermionic Chains
• Quantum transport under oscillatory drive with disordered amplitude
• Superdiffusive transport in chaotic quantum systems with nodal interactions
• Operator entanglement in $\mathrm{SU}(2)$-symmetric dissipative quantum many-body dynamics