{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:TC42FIY3ECGG6WPDOPPT4CMIKN","short_pith_number":"pith:TC42FIY3","schema_version":"1.0","canonical_sha256":"98b9a2a31b208c6f59e373df3e098853502e902393b3827d529707c2672aaa4e","source":{"kind":"arxiv","id":"cond-mat/0407066","version":1},"attestation_state":"computed","paper":{"title":"Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions","license":"","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"F. Verstraete, J. I. Cirac","submitted_at":"2004-07-02T13:09:17Z","abstract_excerpt":"We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We use this result to build powerful numerical simulation techniques to describe the ground state, finite temperature, and evolution of spin systems in two and higher dimensions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"cond-mat/0407066","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.str-el","submitted_at":"2004-07-02T13:09:17Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"92dfc9be93502c15a3c20975ad1a0e28e1779607359537c1becf8952ee4cc8ae","abstract_canon_sha256":"9894372f088f4779a1006da5283545612323c386c74a5e25b2de2ef226f12c1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:21:21.609296Z","signature_b64":"JxM8CPvQAr+70prwAD0GqMdQU9dNRxrBKTb17XV0+enRtplETEH36WYd4PQYAEt/Q0E8fz/MxOGjsdjeIfxxCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98b9a2a31b208c6f59e373df3e098853502e902393b3827d529707c2672aaa4e","last_reissued_at":"2026-07-04T14:21:21.608142Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:21:21.608142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions","license":"","headline":"","cross_cats":["quant-ph"],"primary_cat":"cond-mat.str-el","authors_text":"F. Verstraete, J. I. Cirac","submitted_at":"2004-07-02T13:09:17Z","abstract_excerpt":"We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We use this result to build powerful numerical simulation techniques to describe the ground state, finite temperature, and evolution of spin systems in two and higher dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0407066","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/0407066/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0407066","created_at":"2026-07-04T14:21:21.608216+00:00"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0407066v1","created_at":"2026-07-04T14:21:21.608216+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0407066","created_at":"2026-07-04T14:21:21.608216+00:00"},{"alias_kind":"pith_short_12","alias_value":"TC42FIY3ECGG","created_at":"2026-07-04T14:21:21.608216+00:00"},{"alias_kind":"pith_short_16","alias_value":"TC42FIY3ECGG6WPD","created_at":"2026-07-04T14:21:21.608216+00:00"},{"alias_kind":"pith_short_8","alias_value":"TC42FIY3","created_at":"2026-07-04T14:21:21.608216+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":54,"internal_anchor_count":54,"sample":[{"citing_arxiv_id":"2607.08176","citing_title":"Scalable Simulation of Strongly Correlated Electron-Phonon Systems via Non-Gaussian Matrix Product States","ref_index":72,"is_internal_anchor":true},{"citing_arxiv_id":"2607.05178","citing_title":"Efficient classical simulation of two-dimensional long-range systems: Rydberg arrays and beyond","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"2606.24803","citing_title":"Introduction to matrix-product states and tensor networks","ref_index":20,"is_internal_anchor":true},{"citing_arxiv_id":"2606.23274","citing_title":"Parallelized contraction of tensor trains or matrix product operators","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2606.22816","citing_title":"Isometrization of Tensor Network States via Gauge Propagation","ref_index":18,"is_internal_anchor":true},{"citing_arxiv_id":"2606.23823","citing_title":"Wavelet Matrix Product States for Quantum Fields","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2606.22321","citing_title":"Multi-particle states investigation with tensor renormalization group method","ref_index":23,"is_internal_anchor":true},{"citing_arxiv_id":"2606.20029","citing_title":"A Finite-Volume Scheme for the Continuum Extrapolation of Lattice Step-Scaling in (2+1)D Hamiltonian U(1) Gauge Theory","ref_index":29,"is_internal_anchor":true},{"citing_arxiv_id":"2606.17045","citing_title":"Compact Spin-Charge Separated Neural Quantum States for Valence-Bond States","ref_index":17,"is_internal_anchor":true},{"citing_arxiv_id":"2606.17147","citing_title":"When Renormalisation Remembers: UV/IR Mixing as an Entanglement Bridge","ref_index":32,"is_internal_anchor":true},{"citing_arxiv_id":"2606.08707","citing_title":"Simulating quantum circuits with a neural statebank","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2606.17064","citing_title":"Tensor network compression using fluid dynamics as a testbed: Analytical foundations in one dimension","ref_index":49,"is_internal_anchor":true},{"citing_arxiv_id":"2607.00365","citing_title":"When AI meets quantum information: A comprehensive review","ref_index":232,"is_internal_anchor":true},{"citing_arxiv_id":"2606.04608","citing_title":"Correlated States in Quantum Dot Clusters Coupled to a Common Superconductor","ref_index":30,"is_internal_anchor":true},{"citing_arxiv_id":"2606.31021","citing_title":"Investigation of the $J_1$-$J_2$ Heisenberg model on the triangular lattice: A study with projected entangled-pair states","ref_index":23,"is_internal_anchor":true},{"citing_arxiv_id":"2605.19960","citing_title":"PEPSKit.jl: A Julia package for projected entangled-pair state simulations","ref_index":20,"is_internal_anchor":true},{"citing_arxiv_id":"2605.21597","citing_title":"Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series","ref_index":43,"is_internal_anchor":true},{"citing_arxiv_id":"2605.26208","citing_title":"Mapping twist fields to local operators via tensor networks","ref_index":28,"is_internal_anchor":true},{"citing_arxiv_id":"2605.30429","citing_title":"Attention-based optimizer for symmetry finding","ref_index":19,"is_internal_anchor":true},{"citing_arxiv_id":"1906.10156","citing_title":"Pushing Tensor Networks to the Limit","ref_index":7,"is_internal_anchor":true},{"citing_arxiv_id":"1906.12030","citing_title":"TensorNetwork on TensorFlow: Entanglement Renormalization for quantum critical lattice models","ref_index":11,"is_internal_anchor":true},{"citing_arxiv_id":"2605.22977","citing_title":"Absorbing Many-Body Correlations into Core-Optimized Orbitals","ref_index":82,"is_internal_anchor":true},{"citing_arxiv_id":"2307.15949","citing_title":"Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins","ref_index":18,"is_internal_anchor":true},{"citing_arxiv_id":"2410.19541","citing_title":"The product structure of MPS-under-permutations","ref_index":11,"is_internal_anchor":true},{"citing_arxiv_id":"2502.14091","citing_title":"Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states","ref_index":45,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TC42FIY3ECGG6WPDOPPT4CMIKN","json":"https://pith.science/pith/TC42FIY3ECGG6WPDOPPT4CMIKN.json","graph_json":"https://pith.science/api/pith-number/TC42FIY3ECGG6WPDOPPT4CMIKN/graph.json","events_json":"https://pith.science/api/pith-number/TC42FIY3ECGG6WPDOPPT4CMIKN/events.json","paper":"https://pith.science/paper/TC42FIY3"},"agent_actions":{"view_html":"https://pith.science/pith/TC42FIY3ECGG6WPDOPPT4CMIKN","download_json":"https://pith.science/pith/TC42FIY3ECGG6WPDOPPT4CMIKN.json","view_paper":"https://pith.science/paper/TC42FIY3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cond-mat/0407066&json=true","fetch_graph":"https://pith.science/api/pith-number/TC42FIY3ECGG6WPDOPPT4CMIKN/graph.json","fetch_events":"https://pith.science/api/pith-number/TC42FIY3ECGG6WPDOPPT4CMIKN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TC42FIY3ECGG6WPDOPPT4CMIKN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TC42FIY3ECGG6WPDOPPT4CMIKN/action/storage_attestation","attest_author":"https://pith.science/pith/TC42FIY3ECGG6WPDOPPT4CMIKN/action/author_attestation","sign_citation":"https://pith.science/pith/TC42FIY3ECGG6WPDOPPT4CMIKN/action/citation_signature","submit_replication":"https://pith.science/pith/TC42FIY3ECGG6WPDOPPT4CMIKN/action/replication_record"}},"created_at":"2026-07-04T14:21:21.608216+00:00","updated_at":"2026-07-04T14:21:21.608216+00:00"}