Lowering the temperature of two-dimensional fermionic tensor networks with cluster expansions

• URL: http://arxiv.org/abs/2602.22113v1
• Date: Wed, 25 Feb 2026 16:58:58 GMT
• Title: Lowering the temperature of two-dimensional fermionic tensor networks with cluster expansions
• Authors: Sander De Meyer, Atsushi Ueda, Yuchi He, Nick Bultinck, Jutho Haegeman,
• Abstract summary: Suzuki-Trotter decomposition is the main technique for representing a Hamiltonian composed of strictly short-ranged interactions.<n>We extend the cluster expansion to two-dimensional fermionic systems, and employ it to construct projected entangled-pair operator (PEPO) approximations of Gibbs states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Representing the time-evolution operator as a tensor network constitutes a key ingredient in several algorithms for studying quantum lattice systems at finite temperature or in a non-equilibrium setting. For a Hamiltonian composed of strictly short-ranged interactions, the Suzuki-Trotter decomposition is the main technique for obtaining such a representation. In [B.~Vanhecke, L.~Vanderstraeten and F.~Verstraete, Physical Review A, L020402 (2021)], an alternative strategy, the cluster expansion, was introduced. This approach naturally preserves internal and lattice symmetries and can more easily be extended to higher-order representations or longer-ranged interactions. We extend the cluster expansion to two-dimensional fermionic systems, and employ it to construct projected entangled-pair operator (PEPO) approximations of Gibbs states. We also discuss and benchmark different truncation schemes for multiplying layers of PEPOs together. Applying the resulting framework to a two-dimensional spinless fermion model with attractive interactions, we resolve a clear phase boundary at finite temperature.

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