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.

arXiv comment4+3 pages

References in corpus (25)

• Efficient simulation of one-dimensional quantum many-body systems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Spin diffusion from an inhomogeneous quench in an integrable system
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Super-diffusion in one-dimensional quantum lattice models
• Spectral statistics and many-body quantum chaos with conserved charge
• Integrable Trotterization: Local Conservation Laws and Boundary Driving
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Superdiffusion in spin chains
• Ballistic spin transport in a periodically driven integrable quantum system
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Superuniversality of superdiffusion
• Theory of diffusive fluctuations
• Stability of superdiffusion in nearly integrable spin chains
• Kardar-Parisi-Zhang Scaling for an Integrable Lattice Landau-Lifshitz Spin Chain
• Kardar-Parisi-Zhang physics in integrable rotationally symmetric dynamics on discrete space-time lattice
• Heavy Operators and Hydrodynamic Tails
• Universality classes of spin transport in one-dimensional isotropic magnets: the onset of logarithmic anomalies
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
• Correlations and commuting transfer matrices in integrable unitary circuits
• Integrable Matrix Models in Discrete Space-Time

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• 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