Lowering the temperature of two-dimensional fermionic tensor networks with cluster expansions
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arXiv
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| Format: | Preprint |
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2026
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| author | De Meyer, Sander Ueda, Atsushi He, Yuchi Bultinck, Nick Haegeman, Jutho |
| author_facet | De Meyer, Sander Ueda, Atsushi He, Yuchi Bultinck, Nick Haegeman, Jutho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22113 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lowering the temperature of two-dimensional fermionic tensor networks with cluster expansions De Meyer, Sander Ueda, Atsushi He, Yuchi Bultinck, Nick Haegeman, Jutho Strongly Correlated Electrons Quantum Physics 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. |
| title | Lowering the temperature of two-dimensional fermionic tensor networks with cluster expansions |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2602.22113 |