Kardar-Parisi-Zhang superdiffusion in chaotic quantum circuits
Abstract
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-1/2 (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.
Related
- Kardar--Parisi--Zhang density hydrodynamics in a coherent XXZ--ASEP Lindbladian
- Quantum extreme learning for forecasting experimental chaotic electronic circuits
- Parisi Formula for the ground state energy of quantum p-Spin Hamiltonians
- Superposed quantum evolutions across chaotic and regular regimes
- Temporal entanglement transition in chaotic quantum many-body dynamics
BibTeX
@misc{sharipov2026kardarparisizhang,
title = {{Kardar-Parisi-Zhang superdiffusion in chaotic quantum circuits}},
author = {Rustem Sharipov and Urban Duh and Sun Woo P. Kim and Friedrich Hübner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07143},
eprint = {2610.07143},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07143},
}
RIS
TY - UNPB
TI - Kardar-Parisi-Zhang superdiffusion in chaotic quantum circuits
AU - Rustem Sharipov
AU - Urban Duh
AU - Sun Woo P. Kim
AU - Friedrich Hübner
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07143
UR - https://arxiv.org/abs/2610.07143
AB - 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-1/2 (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.
ER -