{"paper":{"title":"Diagonal Isometric Form for Tensor Network States in Two Dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Incorporating auxiliary tensors creates a diagonal isometric form for two-dimensional tensor product states that supports stable TEBD simulations.","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"Benjamin Sappler, Frank Pollmann, Masataka Kawano, Michael P Zaletel","submitted_at":"2025-07-10T18:00:03Z","abstract_excerpt":"Isometric tensor network states (isoTNS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTNS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation (TEBD) algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demon"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our results demonstrate that isoTPS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That auxiliary tensors can be incorporated to represent the orthogonality hypersurface while preserving the isometric properties required for stable and accurate TEBD contractions in two dimensions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new diagonal isometric representation for 2D isoTPS enables efficient TEBD computation of area-law states and short-time dynamics in the transverse-field Ising model.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Incorporating auxiliary tensors creates a diagonal isometric form for two-dimensional tensor product states that supports stable TEBD simulations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"161b50e2fd6053d3e53a2ca9ad5dcbe95b47d2d21d45036bf5aa8ee9e657fd5a"},"source":{"id":"2507.08080","kind":"arxiv","version":3},"verdict":{"id":"808f6eeb-12e3-49d8-9f60-d941e071a3f8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T05:02:05.961428Z","strongest_claim":"Our results demonstrate that isoTPS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point.","one_line_summary":"A new diagonal isometric representation for 2D isoTPS enables efficient TEBD computation of area-law states and short-time dynamics in the transverse-field Ising model.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That auxiliary tensors can be incorporated to represent the orthogonality hypersurface while preserving the isometric properties required for stable and accurate TEBD contractions in two dimensions.","pith_extraction_headline":"Incorporating auxiliary tensors creates a diagonal isometric form for two-dimensional tensor product states that supports stable TEBD simulations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.08080/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}