Universal scaling of higher-order cumulants in quantum isotropic spin chains

Abstract

Understanding universal behavior of far-from-equilibrium transport dynamics at a quantum many body level is a longstanding challenge. In particular, a full characterization of universal dynamics of nonlocal correlation functions still remains largely unknown. In this letter, we uncover universal scaling laws of higher-order cumulants in one-dimensional isotropic Heisenberg model, revealing anomalous behaviors of nonequilibrium dynamics exclusively accessible in higher-order correlations. By means of numerical simulations and full counting statistics, we determine the power laws of both the spin polarization transfer and contrast cumulants for different kinds of helix and domain-wall initial states. Building on such physical states, we unify the scaling behavior of the higher-order cumulants, giving rise to two types of dynamics: anomalous diffusive and superdiffusive. For the former, these higher cumulants show a deviation from Gaussian statistics, with the scaling exponents being identical for the first four orders. For the latter, however, we observe a breakdown of KPZ universality, with the exponents of the third and fourth orders differing significantly from those of the first two. Our results are also agreeable with recent experimental observations, advancing understanding of far-from-equilibrium transport phenomena.

References in corpus (67)

• Quantum Simulation
• Nonequilibrium dynamics of closed interacting quantum systems
• Level-Spacing Distributions and the Airy Kernel
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• The ITensor Software Library for Tensor Network Calculations
• Time-dependent variational principle for quantum lattices
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Finite-temperature transport in one-dimensional quantum lattice models
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Spin diffusion from an inhomogeneous quench in an integrable system
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Far-from-equilibrium spin transport in Heisenberg quantum magnets
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Super-diffusion in one-dimensional quantum lattice models
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Fibonacci family of dynamical universality classes
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• Superdiffusion in spin chains
• Observing emergent hydrodynamics in a long-range quantum magnet
• Ballistic spin transport in a periodically driven integrable quantum system
• Correlation functions and transport coefficients in generalised hydrodynamics
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Dynamics of magnetization at infinite temperature in a Heisenberg spin chain
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Transport fluctuations in integrable models out of equilibrium
• Catching Bethe phantoms and quantum many-body scars: Long-lived spin-helix states in Heisenberg magnets
• Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Spin-charge separation in a 1D Fermi gas with tunable interactions
• Nonequilibrium Full Counting Statistics and Symmetry-Resolved Entanglement from Space-Time Duality
• Exact anomalous current fluctuations in a deterministic interacting model
• Ballistic macroscopic fluctuation theory
• Absence of Normal Fluctuations in an Integrable Magnet
• Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point
• Performance of the time-dependent variational principle for matrix product states in long-time evolution of a pure state
• Superdiffusive Energy Transport in Kinetically Constrained Models
• Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
• Anomalous transport from hot quasiparticles in interacting spin chains
• Emergence of fluctuating hydrodynamics in chaotic quantum systems
• Full Counting Statistics of Charge in Chaotic Many-body Quantum Systems
• Distinct universality classes of diffusive transport from full counting statistics
• Non-linear fluctuating hydrodynamics for KPZ scaling in isotropic spin chains
• A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model
• Dynamical criticality of magnetization transfer in integrable spin chains
• Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains
• Controlled bond expansion for DMRG ground state search at single-site costs
• Phantom Bethe roots in the integrable open spin $1/2$ $XXZ$ chain
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Diffusive hydrodynamics from long-range correlations
• Dynamics of Spin Helices in the One-Dimensional $XX$ Model
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• Hydrodynamic relaxation of spin helices
• Quantum spin helices more stable than the ground state: onset of helical protection
• Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains
• Universality in relaxation of spin helices under the $XXZ$- spin chain dynamics
• Multi-particle correlations, cumulants, and moments sensitive to fluctuations in rare-probe azimuthal anisotropy in heavy ion collisions
• Probing the Topology of Fermionic Gaussian Mixed States with {U(1)} symmetry by Full Counting Statistics
• Quantum turnstiles for robust measurement of full counting statistics
• Chiral basis for qubits and spin-helix decay
• Exact Entanglement dynamics in Three Interacting Qubits
• Dynamics of spin helices in the diluted one-dimensional $XX$ model
• Cumulants of conserved charges in hydrodynamic simulations
• A unified approach to the thermodynamics and quantum scaling functions of one-dimensional strongly attractive $SU(w)$ Fermi Gases