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arXiv · 2602.15987

Gaussian continuous tensor network states: short-distance properties and imaginary-time evolution

Marco Rigobello·Erez Zohar
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Abstract

We study Gaussian continuous tensor network states (GCTNS) - a finitely-parameterized subclass of Gaussian states admitting an interpretation as continuum limits of discrete tensor network states. We show that, at short distance, GCTNS correspond to free Lifshitz vacua, establishing a connection between certain entanglement properties of the two. Two schemes to approximate ground states of (free) bosonic field theories using GCTNS are presented: rational approximants to the exact dispersion relation and Trotterized imaginary-time evolution. We apply them to Klein-Gordon theory and characterize the resulting approximations, identifying the energy scales at which deviations from the target theory appear. These results provide a simple and analytically controlled setting to assess the strengths and limitations of GCTNS as variational ans\"atze for relativistic quantum fields.

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Marco Rigobello, Erez Zohar. 2026-02-17. Gaussian continuous tensor network states: short-distance properties and imaginary-time evolution. https://arxiv.org/abs/2602.15987

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