Absence of superdiffusion in the quasiperiodic spin chain at weak integrability breaking

Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion

Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate the growth of the mean-square displacement as well as the melting of domain walls. While the system is nonintegrable for all studied parameters, there is no on finite region default of parameters for which we observe diffusive transport. In particular, our model shows a rich dynamical behavior crossing over from superdiffusion to subdiffusion. We discuss the i…

Superdiffusion in spin chains

This review summarizes recent advances in our understanding of anomalous transport in spin chains, viewed through the lens of integrability. Numerical advances, based on tensor-network methods, have shown that transport in many canonical integrable spin chains -- most famously the Heisenberg model -- is anomalous. Concurrently, the framework of generalized hydrodynamics has been extended to explain some of the mechanisms underlying anomalous transport. We present what is currently understood about these mechanisms, and discuss how they resemble (and differ from) the mechanisms for anomalous tr…

Absence of superdiffusion in certain random spin models

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 dyna…

Stability of superdiffusion in nearly integrable spin chains

Superdiffusive finite-temperature transport has been recently observed in a variety of integrable systems with nonabelian global symmetries. Superdiffusion is caused by giant Goldstone-like quasiparticles stabilized by integrability. Here, we argue that these giant quasiparticles remain long-lived, and give divergent contributions to the low-frequency conductivity $σ(ω)$, even in systems that are not perfectly integrable. We find, perturbatively, that $ σ(ω) \sim ω^{-1/3}$ for translation-invariant static perturbations that conserve energy, and $σ(ω) \sim | \log ω|$ for noisy perturbations. Th…

Spin crossovers and superdiffusion in the one-dimensional Hubbard model

We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrat…

微扰易轴海森堡自旋链中扩散常数的标度行为

Scaling of diffusion constants in perturbed easy-axis Heisenberg spin chains

本文通过封闭系统线性响应和开放系统林德布拉德方程等多种方法，研究微扰对易轴海森堡自旋链扩散常数的影响，发现其连续变化及弱微扰下可能发散。