A Universal Approach to Hydrodynamics in Higher Dimensions via Tensor Networks

Abstract

Extracting late-time hydrodynamic transport properties directly from microscopic quantum models, especially in dimensions beyond one, is believed to be classically intractable. This owes, in part, to the extensive growth of entanglement in higher dimensions and often a mismatch between geometric and tensor network locality. Here, we extend the Density Matrix Truncation (DMT) algorithm to accurately and quantitatively predict high-temperature transport coefficients (e.g. diffusion constants) in up to three dimensions. Additionally, we demonstrate the ability to capture the slow crossover dynamics characteristic of weakly broken integrability. The intuition underlying our approach is to preserve the geometrically local information crucial for hydrodynamics throughout the time evolution, despite using a one-dimensional matrix product state ansatz for higher-dimensional calculations. Our work pushes the boundary of classical computability and opens the door to benchmarking the high-temperature, late-time dynamics of generic quantum simulators.