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.

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BibTeX RIS

BibTeX

@misc{anand2026universal,
  title = {{A Universal Approach to Hydrodynamics in Higher Dimensions via Tensor Networks}},
  author = {Sajant Anand and Christopher D. White and Jack Kemp and Julia Wei and Norman Y. Yao and Michael P. Zaletel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40776},
  eprint = {2610.40776},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40776},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - A Universal Approach to Hydrodynamics in Higher Dimensions via Tensor Networks
AU  - Sajant Anand
AU  - Christopher D. White
AU  - Jack Kemp
AU  - Julia Wei
AU  - Norman Y. Yao
AU  - Michael P. Zaletel
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40776
UR  - https://arxiv.org/abs/2610.40776
AB  - 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.
ER  -

Abstract

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