Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far been proposed on fine-tuned, artificial Hamiltonians, posing a significant challenge for experimental observation. In this work, we propose a broad class of models for generating superdiffusion potentially realizable in condensed matter systems across different spatial dimensions. A robust nodal structure emerges from the hybridization between the itinerant electrons and the local impurity orbitals, protected by the intrinsic symmetry and topology of the electronic band. We derive a universal scaling law for the conductance,
G∼L−γ, revealing how the exponent is dictated by the dimensionality of the nodal structure (
Dnode) and its order
n, and the dimensionality of the system
(D) at high temperatures or that of the Fermi surface (
DF) at low temperatures. Through numerical simulations, we validate these scaling relations at zero temperature for various models, including those based on graphene and multi-Weyl semimetals, finding excellent agreement between our theory and the computed exponents. Beyond the scaling of conductance, our framework predicts a suite of experimentally verifiable signatures, notably a new mechanism for linear-in-temperature resistivity (
ρ∼T) and a divergent low-frequency optical conductivity (
σ(ω)∼ωγ−1), establishing a practical route to discovering and engineering anomalous transport in quantum materials.
Investigating the behavior of noninteracting fermions subjected to local dephasing, we reveal that quasi-particle dephasing can induce superdiffusive transport. This superdiffusion arises from nodal points within the momentum distribution of local dephasing quasi-particles, leading to asymptotic long-lived modes. By studying the dynamics of the Wigner function, we rigorously elucidate how the dynamics of these enduring modes give rise to Lévy walk processes, a renowned mechanism underlying superdiffusion phenomena. Our research demonstrates the controllability of dynamical scaling exponents by selecting quasi-particles and extends its applicability to higher dimensions, underlining the pervasive nature of superdiffusion in dephasing models.
We consider a one-dimensional fermionic lattice system with long-ranged power-law decaying hopping with exponent $\ensuremath{\alpha}$. The system is further subjected to dephasing noise in the bulk. We investigate two variants of the problem: (i) an open quantum system where the setup is further subjected to boundary reservoirs enabling the scenario of a nonequilibrium steady-state charge transport, and (ii) time dynamics of an initially localized single-particle excitation in the absence of boundary reservoirs. In both variants, anomalous superdiffusive behavior is observed for $1<\ensuremath{\alpha}<1.5$, and for $\ensuremath{\alpha}>1.5$ the setup is effectively short ranged and exhibits conventional diffusive transport. Our findings are supported by analytical calculations based on the multiple scale analysis technique that leads to the emergence of a fractional diffusion equation for the density profile. Our study unravels an interesting interplay between long-range interaction and dephasing mechanism that could result in the emergence of unconventional behavior in open quantum systems.
We construct a family of chaotic brickwork quantum circuits exhibiting superdiffusive transport with dynamical exponent
z=3/2 in the full Kardar--Parisi--Zhang (KPZ) universality class. This is enabled by the equilibrium current associated with a inhomogeneous conserved density having a nontrivial dependence on the chemical potential. Using nonlinear fluctuating hydrodynamics, we derive the propagation velocity, broadening scale, and universal scaling form of the charge correlation function from microscopic equilibrium properties. Tensor-network simulations of a two-site spin-
1 (qutrit) circuit reproduce these parameter-free predictions, including the full stationary KPZ profile. We further construct a three-site spin-
21 (qubit) circuit, where transport varies from diffusive to superdiffusive with the chemical potential, while long-lived coherent quasiparticles delay the convergence of the profile to the KPZ scaling form. Our results establish that KPZ superdiffusion in quantum systems is not restricted to fine-tuned integrable models.
We identify a class of one-dimensional spin and fermionic lattice models that display diverging spin and charge diffusion constants, including several paradigmatic models of exactly solvable, strongly correlated many-body dynamics such as the isotropic Heisenberg spin chains, the Fermi-Hubbard model, and the t-J model at the integrable point. Using the hydrodynamic transport theory, we derive an analytic lower bound on the spin and charge diffusion constants by calculating the curvature of the corresponding Drude weights at half-filling, and demonstrate that for certain lattice models with isotropic interactions some of the Noether charges exhibit superdiffusive transport at finite temperature and half-filling.
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 with local interactions, 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 the dynamical exponent z ¼ 3=2.This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: We accordingly dub it "superuniversal."The anomalous transport behavior is attributed to long-lived giant quasiparticles dressed by thermal fluctuations.We provide an algebraic viewpoint on the corresponding dressing transformation and elucidate formal connections to fusion identities amongst the quantum-group characters.We identify giant quasiparticles with nonlinear soliton modes of classical field theories that describe low-energy excitations above ferromagnetic vacua.Our analysis of these field theories also provides a complete classification of the low-energy (i.e., Goldstone-mode) spectra of quantum isotropic ferromagnetic chains.