{"arxiv_id":"1308.1960","incoming":{"papers":11,"sentences":72,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1501.07603","title":"Dynamical Casimir Effect in a small compact manifold for the Maxwell vacuum","url":"/paper/1501.07603","section":"External static magnetic field","sentence":"Therefore, the partition function in the presence of the uniform magnetic field can be easily reconstructed from ([ref]), and it is given by [ref]","intent_p":0.89,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":2,"sentences":4,"quotes":[{"arxiv_id":"1501.07603","title":"Dynamical Casimir Effect in a small compact manifold for the Maxwell vacuum","url":"/paper/1501.07603","section":"Construction","sentence":"With these additional simplifications the topological partition function becomes [ref] :","intent_p":0.8,"contests_p":null},{"arxiv_id":"1407.3804","title":"Topological order and Berry connection for the Maxwell Vacuum on a four-torus","url":"/paper/1407.3804","section":"Construction","sentence":"We follow [ref] in our construction of the partition function $Z_top$ where it was employed for computation of the corrections to the Casimir effect due to these novel type of topological fluctuations.","intent_p":0.99,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1511.02028","title":"Hagedorn transition and topological entanglement entropy","url":"/paper/1511.02028","section":"2D modular formulae and high-temperature continuation","sentence":"After the expansion ([ref]) is obtained, we can substitute $τ=β/4πR$ and get [equation] We notice that similar expressions also appear in weak-coupling calculation on a different manifold [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":3,"sentences":8,"quotes":[{"arxiv_id":"1407.3804","title":"Topological order and Berry connection for the Maxwell Vacuum on a four-torus","url":"/paper/1407.3804","section":"Introduction. Motivation.","sentence":"Such a similarity looks very instructive and suggestive, and further supports our arguments [ref] that the ground state of the Maxwell theory defined on a small compact manifold behaves as a TQFT.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1501.07603","title":"Dynamical Casimir Effect in a small compact manifold for the Maxwell vacuum","url":"/paper/1501.07603","section":"Introduction. Motivation.","sentence":"In particular, $Z_top$ demonstrates the degeneracy of the system which can not be described in terms of any local operators [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1310.2258","title":"Inflaton as an auxiliary topological field in a QCD-like system","url":"/paper/1310.2258","section":"Topological auxiliary field as a source of the “strange\" energy","sentence":"In fact, this conjecture is supported in some way by computations in a simplified model [ref] , see also [ref] with related discussions.].","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":2,"sentences":3,"quotes":[{"arxiv_id":"1512.00470","title":"Aharonov-Bohm phases in a quantum LC circuit","url":"/paper/1512.00470","section":"Introduction. Motivation.","sentence":"In section [ref], we review the construction of magnetic-type instantons and the partition function $Z_top$ in [ref] .","intent_p":0.83,"contests_p":null},{"arxiv_id":"1407.3804","title":"Topological order and Berry connection for the Maxwell Vacuum on a four-torus","url":"/paper/1407.3804","section":"Berry phase in CM systems","sentence":"In context of the topological insulators and quantum Hall systems the corresponding studies have been carried out in two, three and four dimensions [ref] , see also [ref] with related discussions of the ground state in 2d Maxwell theory[Not to be confused with conventional CM notations, where it is a customary to count the spatial number of dimensions, rather than total number of dimensions.","intent_p":0.95,"contests_p":null}]}],"unlabelled_sentences":55},"outgoing":{"papers":19,"sentences":81,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":5,"sentences":7,"quotes":[{"arxiv_id":"cond-mat/0404327","title":"Superconductors are topologically ordered","url":"/paper/cond-mat/0404327","section":"Partition function in “BF\" formulation","sentence":"We wish to derive the topological action for the Maxwell system by using the same conventional technique exploited e.g. in [ref] for the so-called “deformed QCD\" and in [ref] for the Higgs model.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1301.7072","title":"QCD as a topologically ordered system","url":"/paper/1301.7072","section":"Partition function in “BF\" formulation","sentence":"We wish to derive the topological action for the Maxwell system by using the same conventional technique exploited e.g. in [ref] for the so-called “deformed QCD\" and in [ref] for the Higgs model.","intent_p":1.0,"contests_p":null},{"arxiv_id":"hep-th/9508142","title":"Generalized Thirring Models","url":"/paper/hep-th/9508142","section":"Partition function","sentence":"All integrals in this partition function are gaussian and can be easily evaluated using the technique developed in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1301.1706","title":"Topological Casimir effect in Maxwell Electrodynamics on a Compact Manifold","url":"/paper/1301.1706","section":"Topological partition function $Z_top$.","sentence":"We follow [ref] in our construction of the partition function $Z_top$ where it was employed for computation of the corrections to the Casimir effect due to these novel type of topological fluctuations.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1206.5831","title":"Do gauge fields really contribute negatively to black hole entropy?","url":"/paper/1206.5831","section":"Entropy in 2d Maxwell system","sentence":"Appropriate treatment has been suggested in [ref] by defining the system in a large box size $V$.","intent_p":0.91,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":5,"sentences":6,"quotes":[{"arxiv_id":"1204.4653","title":"Remarks on the thermodynamics and the vacuum energy of a quantum Maxwell gas on compact and closed manifolds","url":"/paper/1204.4653","section":"Degeneracy at $θ_eff=π$","sentence":"[ref] in the presence of the electric fluxes.","intent_p":0.95,"contests_p":null},{"arxiv_id":"cond-mat/0404327","title":"Superconductors are topologically ordered","url":"/paper/cond-mat/0404327","section":"“BF\" formulation of the Maxwell system","sentence":"Therefore, these massless photons can be completely ignored in our studies of the topological properties of the partition function, similar to decoupling of the massless phonons (which are in fact responsible for the mere existence of a gap) in treatment of the topologically ordered superconductors [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"1210.1281","title":"Topological order: from long-range entangled quantum matter to an unification of light and electrons","url":"/paper/1210.1281","section":"Similarities and differences between TE and Topological Entanglement Entropy in CM systems","sentence":"-lnD=- χ_mag (τ≫1 )/2 =-1/2 ⟶ D=√(e), which should be compared with conventional $D=√(m)$ for a Laughlin state in a fractional quantum Hall system with filling factor $ν=1/m$, or $D=2$ for $p+ip$ superconductor, or any other similar systems, see recent reviews [ref] for the details and original references.","intent_p":0.81,"contests_p":null},{"arxiv_id":"1203.4565","title":"The quantum phases of matter","url":"/paper/1203.4565","section":"Similarities and differences between TE and Topological Entanglement Entropy in CM systems","sentence":"-lnD=- χ_mag (τ≫1 )/2 =-1/2 ⟶ D=√(e), which should be compared with conventional $D=√(m)$ for a Laughlin state in a fractional quantum Hall system with filling factor $ν=1/m$, or $D=2$ for $p+ip$ superconductor, or any other similar systems, see recent reviews [ref] for the details and original references.","intent_p":0.81,"contests_p":null},{"arxiv_id":"1012.2084","title":"Topological Insulator and the $\\theta$-vacuum in a system without boundaries","url":"/paper/1012.2084","section":"Topological partition function $Z_top$.","sentence":"[ref] arrived to the same conclusion (on decoupling of the topological terms from conventional fluctuating photons with non-zero momentum), though in a different context of topological insulators in the presence of the $θ=π$ term.","intent_p":0.85,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":2,"sentences":3,"quotes":[{"arxiv_id":"1301.1706","title":"Topological Casimir effect in Maxwell Electrodynamics on a Compact Manifold","url":"/paper/1301.1706","section":"Introduction. Motivation.","sentence":"In particular, it has been explicitly shown in [ref] that these novel terms lead to a fundamentally new contributions to the Casimir vacuum pressure, which can not be expressed in terms of conventional propagating physical degrees of freedom.","intent_p":0.99,"contests_p":null},{"arxiv_id":"1206.5831","title":"Do gauge fields really contribute negatively to black hole entropy?","url":"/paper/1206.5831","section":"Entropy in 2d Maxwell system","sentence":"Furthermore, the entropy ([ref]) is obviously a positively defined function at any finite $V$ and can be interpreted as the entanglement entropy [ref] .","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":6,"sentences":6,"quotes":[{"arxiv_id":"1209.2677","title":"Remarks on effective action and entanglement entropy of Maxwell field in generic gauge","url":"/paper/1209.2677","section":"Topological Entropy in Maxwell theory in four dimensions","sentence":"The entanglement entropy for Maxwell theory is also known, see recent paper [ref] with many references on previous works therein.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1011.3485","title":"Topological BF field theory description of topological insulators","url":"/paper/1011.3485","section":"Introduction. Motivation.","sentence":"Furthermore, it demonstrates many features of topologically ordered systems, which were initially introduced in context of condensed matter systems, see original papers [ref] and recent reviews [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"1210.1281","title":"Topological order: from long-range entangled quantum matter to an unification of light and electrons","url":"/paper/1210.1281","section":"Introduction. Motivation.","sentence":"Furthermore, it demonstrates many features of topologically ordered systems, which were initially introduced in context of condensed matter systems, see original papers [ref] and recent reviews [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"cond-mat/0404327","title":"Superconductors are topologically ordered","url":"/paper/cond-mat/0404327","section":"Introduction. Motivation.","sentence":"Furthermore, it demonstrates many features of topologically ordered systems, which were initially introduced in context of condensed matter systems, see original papers [ref] and recent reviews [ref] .","intent_p":0.84,"contests_p":null},{"arxiv_id":"1203.4565","title":"The quantum phases of matter","url":"/paper/1203.4565","section":"Introduction. Motivation.","sentence":"Furthermore, it demonstrates many features of topologically ordered systems, which were initially introduced in context of condensed matter systems, see original papers [ref] and recent reviews [ref] .","intent_p":0.84,"contests_p":null}]}],"unlabelled_sentences":59},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/1308.1960"}}