Superdiffusion from emergent classical solitons in quantum spin chains

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…

各向同性自旋链中从超扩散到扩散的缓慢渡越

Slow crossover from superdiffusion to diffusion in isotropic spin chains

本文用离散时间经典模型模拟噪声与Floquet各向同性微扰，发现自旋链超扩散转向扩散的时间尺度随λ^-6增长，并以大孤立子寿命的动理学理论解释。

Quantum solitons with emergent interactions in a model of cold atoms on the triangular lattice

Cold atoms bring new opportunities to study quantum magnetism, and in particular, to simulate quantum magnets with symmetry greater than $SU(2)$. Here we explore the topological excitations which arise in a model of cold atoms on the triangular lattice with $SU(3)$ symmetry. Using a combination of homotopy analysis and analytic field-theory we identify a new family of solitonic wave functions characterised by integer charge ${\bf Q} = (Q_A, Q_B, Q_C)$, with $Q_A + Q_B + Q_C = 0$. We use a numerical approach, based on a variational wave function, to explore the stability of these solitons on a …

Superuniversality of superdiffusion

Anomalous finite-temperature transport has recently been observed in numerical studies of various integrable models in one dimension; these models share the feature of being invariant under a continuous non-abelian global symmetry. This work offers a comprehensive group-theoretic account of this elusive phenomenon. For an integrable quantum model invariant under a global non-abelian simple Lie group $G$, we find that finite-temperature transport of Noether charges associated with symmetry $G$ in thermal states that are invariant under $G$ is universally superdiffusive and characterized by dyna…

近可积量子气体的Chapman-Enskog理论及扩散与超扩散之间的交叉

Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases

该研究针对弱破坏可积性的近可积伽利略不变量子气体系统，通过带碰撞项的广义流体力学方程与适配的Chapman-Enskog展开，推导了不同尺度下的输运行为与交叉尺度，明确了从Navier-Stokes输运到KPZ普适类的渡越规律。

在CoNb₂O₆中涌现D₈⁽¹⁾谱和拓扑孤子激发

Emergent $D_8^{(1)}$ spectrum and topological soliton excitation in CoNb$_2$O$_6$

研究发现CoNb₂O₆在量子临界点附近表现出D₈⁽¹⁾代数结构的谱特征及拓扑孤子激发，拓展了量子临界系统中可积性和拓扑激发的研究。