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

• URL: http://arxiv.org/abs/2602.15987v1
• Date: Tue, 17 Feb 2026 20:24:19 GMT
• Title: Gaussian continuous tensor network states: short-distance properties and imaginary-time evolution
• Authors: Marco Rigobello, Erez Zohar,
• Abstract summary: We show that GCTNS correspond to free Lifshitz vacua, establishing a connection between certain entanglement properties of the two.<n>Two schemes to approximate ground states of (free) bosonic field theories using GCTNS are presented.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 ansätze for relativistic quantum fields.

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