{"work":{"id":"c0fbf088-e4ab-4ecd-a8a2-6ca647d26e13","openalex_id":null,"doi":null,"arxiv_id":"hep-th/0405152","raw_key":null,"title":"Entanglement Entropy and Quantum Field Theory","authors":null,"authors_text":"P","year":2004,"venue":"hep-th","abstract":"We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy S_A=-Tr rho_A log rho_A corresponding to the reduced density matrix rho_A of a subsystem A. For the case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, we re-derive the result S_A\\sim(c/3) log(l) of Holzhey et al. when A is a finite interval of length l in an infinite system, and extend it to many other cases: finite systems,finite temperatures, and when A consists of an arbitrary number of disjoint intervals. For such a system away from its critical point, when the correlation length \\xi is large but finite, we show that S_A\\sim{\\cal A}(c/6)\\log\\xi, where \\cal A is the number of boundary points of A. These results are verified for a free massive field theory, which is also used to confirm a scaling ansatz for the case of finite-size off-critical systems, and for integrable lattice models, such as the Ising and XXZ models, which are solvable by corner transfer matrix methods. Finally the free-field results are extended to higher dimensions, and used to motivate a scaling form for the singular part of the entanglement entropy near a quantum phase transition.","external_url":"https://arxiv.org/abs/hep-th/0405152","cited_by_count":null,"metadata_source":"pith","metadata_fetched_at":"2026-05-25T20:07:08.376737+00:00","pith_arxiv_id":"hep-th/0405152","created_at":"2026-05-10T01:10:09.221382+00:00","updated_at":"2026-05-25T20:07:08.376737+00:00","title_quality_ok":true,"display_title":"Calabrese and J.L","render_title":"Calabrese and J.L"},"hub":{"state":{"work_id":"c0fbf088-e4ab-4ecd-a8a2-6ca647d26e13","tier":"hub","tier_reason":"10+ Pith inbound or 1,000+ external citations","pith_inbound_count":24,"external_cited_by_count":null,"distinct_field_count":5,"first_pith_cited_at":"2019-06-19T18:00:17+00:00","last_pith_cited_at":"2026-05-20T14:41:16+00:00","author_build_status":"not_needed","summary_status":"needed","contexts_status":"needed","graph_status":"needed","ask_index_status":"not_needed","reader_status":"not_needed","recognition_status":"not_needed","updated_at":"2026-05-27T21:07:57.203458+00:00","tier_text":"hub"},"tier":"hub","role_counts":[{"context_role":"background","n":10}],"polarity_counts":[{"context_polarity":"background","n":9},{"context_polarity":"support","n":1}],"runs":{},"summary":{},"graph":{},"authors":[]}}