Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems

Abstract

Although the Bethe ansatz solution of the spin-1/2 Heisenberg model dates back nearly a century, the anomalous nature of its high-temperature transport dynamics has only recently been uncovered. Indeed, numerical and experimental observations have demonstrated that spin transport in this paradigmatic model falls into the Kardar-Parisi-Zhang (KPZ) universality class. This has inspired the significantly stronger conjecture that KPZ dynamics, in fact, occur in all integrable spin chains with non-Abelian symmetry. Here, we provide extensive numerical evidence affirming this conjecture. Moreover, we observe that KPZ transport is even more generic, arising in both supersymmetric and periodically-driven models. Motivated by recent advances in the realization of SU(N)-symmetric spin models in alkaline-earth-based optical lattice experiments, we propose and analyze a protocol to directly investigate the KPZ scaling function in such systems.

7+13 pages, 3+13 figures

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• Dynamical criticality of magnetization transfer in integrable spin chains
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
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• Comparing numerical methods for hydrodynamics in a one-dimensional lattice spin model
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• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• Efficient computation of cumulant evolution and full counting statistics: application to infinite temperature quantum spin chains
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• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Emergent non-Hermitian conservation laws at exceptional points
• Family-Vicsek universality of the binary intrinsic dimension of nonequilibrium data
• Universal scaling of higher-order cumulants in quantum isotropic spin chains