Quantum

A Universal Approach to Hydrodynamics in Higher Dimensions via Tensor Networks

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Briefings

A new method using Density Matrix Truncation (DMT) successfully predicts high-temperature transport coefficients in up to three dimensions by preserving geometric locality in a one-dimensional matrix product state ansatz. This approach resolves the classical intractability of extracting late-time hydrodynamic properties from microscopic quantum models in higher dimensions.

Key points

• The study extends the Density Matrix Truncation (DMT) algorithm to quantitatively predict diffusion constants in three dimensions.
• The method captures slow crossover dynamics characteristic of weakly broken integrability systems.

Context

This research addresses a fundamental challenge in quantum many-body physics where high-dimensional entanglement and geometric-tensor network locality mismatches prevent direct calculation of late-time transport properties. The work provides a benchmark for quantum simulators and extends classical computability in high-dimensional systems.

Limitations

The study is limited to three dimensions and focuses on high-temperature transport coefficients. It does not provide data on lower dimensions or specific low-temperature regimes. The results are based on a preprint and remain subject to verification.

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