Dynamics of magnetization at infinite temperature in a Heisenberg spin chain

Abstract

Understanding universal aspects of quantum dynamics is an unresolved problem in statistical mechanics. In particular, the spin dynamics of the 1D Heisenberg model were conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution, $P(\mathcal{M})$, of the magnetization transferred across the chain's center. The first two moments of $P(\mathcal{M})$ show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.

References in corpus (65)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Nonequilibrium dynamics of closed interacting quantum systems
• Efficient classical simulation of slightly entangled quantum computations
• Strong quantum computational advantage using a superconducting quantum processor
• Shape Fluctuations and Random Matrices
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• A class of quantum many-body states that can be efficiently simulated
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Time evolution of local observables after quenching to an integrable model
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Algorithms for entanglement renormalization
• Hydrodynamic Diffusion in Integrable Systems
• Demonstrating a Continuous Set of Two-qubit Gates for Near-term Quantum Algorithms
• Spin diffusion from an inhomogeneous quench in an integrable system
• Universal Spin Transport in a Strongly Interacting Fermi Gas
• Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
• Bethe-Boltzmann Hydrodynamics and Spin Transport in the XXZ Chain
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Exact scaling functions for one-dimensional stationary KPZ growth
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Solvable Hydrodynamics of Quantum Integrable Systems
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Kinetic theory of spin diffusion and superdiffusion in XXZ spin chains
• Observation of universal dynamics in an isolated one-dimensional Bose gas far from equilibrium
• Super-diffusion in one-dimensional quantum lattice models
• Measurement-induced entanglement and teleportation on a noisy quantum processor
• Spin dynamics and transport in gapped one-dimensional Heisenberg antiferromagnets at nonzero temperatures
• A note on generalized hydrodynamics: inhomogeneous fields and other concepts
• 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
• Observation of KPZ universal scaling in a one-dimensional polariton condensate
• Low temperature spin diffusion in the one-dimensional quantum $O(3)$ nonlinear $\sigma$-model
• Observing emergent hydrodynamics in a long-range quantum magnet
• Ballistic spin transport in a periodically driven integrable quantum system
• Hydrodynamic long-time tails after a quantum quench
• Anomalous spin diffusion in one-dimensional antiferromagnets
• Universal spin dynamics in infinite-temperature one-dimensional quantum magnets
• Superuniversality of superdiffusion
• Superdiffusion from emergent classical solitons in quantum spin chains
• Kardar-Parisi-Zhang universality from soft gauge modes
• Emergent hydrodynamics in a strongly interacting dipolar spin ensemble
• Dynamics of the spin-1/2 Heisenberg chain initialized in a domain-wall state
• Formation of robust bound states of interacting microwave photons
• Kardar-Parisi-Zhang Scaling for an Integrable Lattice Landau-Lifshitz Spin Chain
• Anomalous relaxation and the high-temperature structure factor of XXZ spin chains
• Accurately computing electronic properties of a quantum ring
• Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
• High-precision simulation of the height distribution for the KPZ equation
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Absence of Normal Fluctuations in an Integrable Magnet
• Correlations and commuting transfer matrices in integrable unitary circuits
• Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
• Anomalous transport from hot quasiparticles in interacting spin chains
• Integrable Matrix Models in Discrete Space-Time
• 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
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
• Anomalous and regular transport in spin 1/2 chains: AC conductivity
• Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet

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