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Volumn 2006, Issue , 2006, Pages

Szegö limit theorem for operators with discontinuous symbols and applications to entanglement entropy

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EID: 33845881967     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1155/IMRN/2006/95181     Document Type: Article
Times cited : (18)

References (44)
  • 1
    • 33748658295 scopus 로고    scopus 로고
    • Entanglement scaling in critical two-dimensional fermionic and bosonic systems
    • 022329 pages
    • T. Barthel M.-C. Chung U. Schollwöck Entanglement scaling in critical two-dimensional fermionic and bosonic systems. Physical Review A 74 2006 2 022329 5 pages
    • (2006) Physical Review A , vol.74 , Issue.2 , pp. 5
    • Barthel, T.1    Chung, M.-C.2    Schollwöck, U.3
  • 2
    • 0000000598 scopus 로고
    • A localization theorem for Toeplitz determinants
    • E. L. Basor A localization theorem for Toeplitz determinants. Indiana University Mathematics Journal 28 1979 6 975 983
    • (1979) Indiana University Mathematics Journal , vol.28 , Issue.6 , pp. 975-983
    • Basor, E.L.1
  • 3
    • 3042719196 scopus 로고
    • The Fisher-Hartwig conjecture and generalizations
    • E. L. Basor C. A. Tracy The Fisher-Hartwig conjecture and generalizations. Physica A 177 1991 1-3 167 173
    • (1991) Physica A , vol.177 , Issue.1-3 , pp. 167-173
    • Basor, E.L.1    Tracy, C.A.2
  • 5
    • 0034673710 scopus 로고    scopus 로고
    • Quantum information and computation
    • C. H. Bennett D. P. DiVincenzo Quantum information and computation. Nature 2000 404 6775 247 255
    • (2000) Nature , vol.404 , Issue.6775 , pp. 247-255
    • Bennett, C.H.1    Divincenzo, D.P.2
  • 7
    • 21844500668 scopus 로고
    • The Onsager formula, the Fisher-Hartwig conjecture, and their influence on research into Toeplitz operators
    • papers dedicated to the memory of L. Onsager
    • A. Böttcher The Onsager formula, the Fisher-Hartwig conjecture, and their influence on research into Toeplitz operators. papers dedicated to the memory of L. Onsager Journal of Statistical Physics 78 1995 1-2 575 584
    • (1995) Journal of Statistical Physics , vol.78 , Issue.1-2 , pp. 575-584
    • Böttcher, A.1
  • 8
    • 0009122713 scopus 로고    scopus 로고
    • Average decay of Fourier transforms and integer points in polyhedra
    • L. Brandolini L. Colzani G. Travaglini Average decay of Fourier transforms and integer points in polyhedra. Arkiv för Matematik 35 1997 2 253 275
    • (1997) Arkiv för Matematik , vol.35 , Issue.2 , pp. 253-275
    • Brandolini, L.1    Colzani, L.2    Travaglini, G.3
  • 10
    • 33845868907 scopus 로고
    • Regularly varying rates of decrease for moduli of continuity and Fourier transforms of functions on d
    • D. B. H. Cline Regularly varying rates of decrease for moduli of continuity and Fourier transforms of functions on d. Journal of Mathematical Analysis and Applications 159 1991 2 507 519
    • (1991) Journal of Mathematical Analysis and Applications , vol.159 , Issue.2 , pp. 507-519
    • Cline, D.B.H.1
  • 11
    • 0013247924 scopus 로고    scopus 로고
    • A status report on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities
    • Oper. Theory Adv. Appl. Birkhäuser Basel
    • T. Ehrhardt A status report on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities. Recent Advances in Operator Theory (Groningen, 1998) Oper. Theory Adv. Appl. 124 217 241 Birkhäuser Basel 2001
    • (2001) Recent Advances in Operator Theory (Groningen, 1998) , vol.124 , pp. 217-241
    • Ehrhardt, T.1
  • 12
    • 0345149787 scopus 로고    scopus 로고
    • Entropy growth of shift-invariant states on a quantum spin chain
    • M. Fannes B. Haegeman M. Mosonyi Entropy growth of shift-invariant states on a quantum spin chain. Journal of Mathematical Physics 44 2003 12 6005 6019
    • (2003) Journal of Mathematical Physics , vol.44 , Issue.12 , pp. 6005-6019
    • Fannes, M.1    Haegeman, B.2    Mosonyi, M.3
  • 15
    • 0141526077 scopus 로고    scopus 로고
    • Lower order terms in Szegö type limit theorems on Zoll manifolds
    • D. Gioev Lower order terms in Szegö type limit theorems on Zoll manifolds. Communications in Partial Differential Equations 28 2003 9-10 1739 1785
    • (2003) Communications in Partial Differential Equations , vol.28 , Issue.9-10 , pp. 1739-1785
    • Gioev, D.1
  • 17
    • 33644887514 scopus 로고    scopus 로고
    • Entanglement entropy of fermions in any dimension and the Widom conjecture
    • 100503 pages
    • D. Gioev I. Klich Entanglement entropy of fermions in any dimension and the Widom conjecture. Physical Review Letters 96 2006 10 100503 4 pages
    • (2006) Physical Review Letters , vol.96 , Issue.10 , pp. 4
    • Gioev, D.1    Klich, I.2
  • 18
    • 0003897671 scopus 로고
    • London Mathematical Society Lecture Note Series Cambridge University Press Cambridge
    • A. Grigis J. Sjöstrand Microlocal Analysis for Differential Operators. London Mathematical Society Lecture Note Series 196 Cambridge University Press Cambridge 1994 iv+151
    • (1994) Microlocal Analysis for Differential Operators , vol.196
    • Grigis, A.1    Sjöstrand, J.2
  • 19
    • 0031164791 scopus 로고    scopus 로고
    • Spectral asymptotics of Toeplitz operators on Zoll manifolds
    • V. Guillemin K. Okikiolu Spectral asymptotics of Toeplitz operators on Zoll manifolds. Journal of Functional Analysis 146 1997 2 496 516
    • (1997) Journal of Functional Analysis , vol.146 , Issue.2 , pp. 496-516
    • Guillemin, V.1    Okikiolu, K.2
  • 20
    • 33344464491 scopus 로고    scopus 로고
    • Bipartite entanglement and entropic boundary law in lattice spin systems
    • 022315 pages
    • A. Hamma R. Ionicioiu P. Zanardi Bipartite entanglement and entropic boundary law in lattice spin systems. Physical Review A 2005 71 2 022315 10 pages
    • (2005) Physical Review A , vol.71 , Issue.2 , pp. 10
    • Hamma, A.1    Ionicioiu, R.2    Zanardi, P.3
  • 22
    • 4043058415 scopus 로고    scopus 로고
    • Quantum spin chain, Toeplitz determinants and the Fisher-Hartwig conjecture
    • B.-Q. Jin V. E. Korepin Quantum spin chain, Toeplitz determinants and the Fisher-Hartwig conjecture. Journal of Statistical Physics 116 2004 1-4 79 95
    • (2004) Journal of Statistical Physics , vol.116 , Issue.1-4 , pp. 79-95
    • Jin, B.-Q.1    Korepin, V.E.2
  • 23
    • 11244310555 scopus 로고    scopus 로고
    • Random matrix theory and entanglement in quantum spin chains
    • J. P. Keating F. Mezzadri Random matrix theory and entanglement in quantum spin chains. Communications in Mathematical Physics 252 2004 1-3 543 579
    • (2004) Communications in Mathematical Physics , vol.252 , Issue.1-3 , pp. 543-579
    • Keating, J.P.1    Mezzadri, F.2
  • 24
    • 18144411651 scopus 로고    scopus 로고
    • Entanglement in quantum spin chains, symmetry classes of random matrices, and conformal field theory
    • 050501 pages
    • J. P. Keating F. Mezzadri Entanglement in quantum spin chains, symmetry classes of random matrices, and conformal field theory. Physical Review Letters 94 2005 5 050501 4 pages
    • (2005) Physical Review Letters , vol.94 , Issue.5 , pp. 4
    • Keating, J.P.1    Mezzadri, F.2
  • 25
    • 30644470279 scopus 로고    scopus 로고
    • Lower entropy bounds and particle number fluctuations in a Fermi sea
    • I. Klich Lower entropy bounds and particle number fluctuations in a Fermi sea. Journal of Physics A 39 2006 4 L85 L91
    • (2006) Journal of Physics A , vol.39 , Issue.4
    • Klich, I.1
  • 26
    • 2442560099 scopus 로고    scopus 로고
    • Universality of entropy scaling in one dimensional gapless models
    • 096402 pages
    • V. E. Korepin Universality of entropy scaling in one dimensional gapless models. Physical Review Letters 2004 92 9 096402 3 pages
    • (2004) Physical Review Letters , vol.92 , Issue.9 , pp. 3
    • Korepin, V.E.1
  • 28
    • 33846881659 scopus 로고    scopus 로고
    • Scaling behavior of entanglement in two- and three-dimensional free fermion systems
    • 073103 pages
    • W. Li L. Ding R. Yu T. Roscilde S. Haas Scaling behavior of entanglement in two- and three-dimensional free fermion systems. Physical Review B 74 2006 7 073103 4 pages
    • (2006) Physical Review B , vol.74 , Issue.7 , pp. 4
    • Li, W.1    Ding, L.2    Yu, R.3    Roscilde, T.4    Haas, S.5
  • 29
    • 0035939387 scopus 로고    scopus 로고
    • Good dynamics versus bad kinematics: Is entanglement needed for quantum computation?
    • 047901 pages
    • N. Linden S. Popescu Good dynamics versus bad kinematics: is entanglement needed for quantum computation? Physical Review Letters 2001 87 4 047901 4 pages
    • (2001) Physical Review Letters , vol.87 , Issue.4 , pp. 4
    • Linden, N.1    Popescu, S.2
  • 31
    • 0036757880 scopus 로고    scopus 로고
    • Entanglement in a simple quantum phase transition
    • 032110 pages
    • T. J. Osborne M. A. Nielsen Entanglement in a simple quantum phase transition. Physical Review A 66 2002 3 032110 14 pages
    • (2002) Physical Review A , vol.66 , Issue.3 , pp. 14
    • Osborne, T.J.1    Nielsen, M.A.2
  • 32
    • 0037061511 scopus 로고    scopus 로고
    • Scaling of entanglement close to a quantum phase transition
    • A. Osterloh L. Amico G. Falci R. Fazio Scaling of entanglement close to a quantum phase transition. Nature 2002 416 6881 608 610
    • (2002) Nature , vol.416 , Issue.6881 , pp. 608-610
    • Osterloh, A.1    Amico, L.2    Falci, G.3    Fazio, R.4
  • 33
    • 0004150286 scopus 로고
    • Fundamental Theories of Physics Kluwer Academic Dordrecht
    • A. Peres Quantum Theory: Concepts and Methods. Fundamental Theories of Physics 57 Kluwer Academic Dordrecht 1993 xiv+446
    • (1993) Quantum Theory: Concepts and Methods , vol.57
    • Peres, A.1
  • 34
    • 18144421896 scopus 로고    scopus 로고
    • Entropy, entanglement, and area: Analytical results for harmonic lattice systems
    • 060503 pages
    • M. B. Plenio J. Eisert J. Dreiig M. Cramer Entropy, entanglement, and area: analytical results for harmonic lattice systems. Physical Review Letters 94 2005 6 060503 4 pages
    • (2005) Physical Review Letters , vol.94 , Issue.6 , pp. 4
    • Plenio, M.B.1    Eisert, J.2    Dreiig, J.3    Cramer, M.4
  • 36
    • 0000359705 scopus 로고
    • Ein Grenzwertsatz über die Toeplitzschen Determinanten einer reellen positiven Funktion
    • G. Szegö Ein Grenzwertsatz über die Toeplitzschen Determinanten einer reellen positiven Funktion. Mathematische Annalen 76 1915 4 490 503
    • (1915) Mathematische Annalen , vol.76 , Issue.4 , pp. 490-503
    • Szegö, G.1
  • 37
    • 0242425255 scopus 로고    scopus 로고
    • Efficient classical simulation of slightly entangled quantum computations
    • 147902 pages
    • G. Vidal Efficient classical simulation of slightly entangled quantum computations. Physical Review Letters 2003 91 14 147902 4 pages
    • (2003) Physical Review Letters , vol.91 , Issue.14 , pp. 4
    • Vidal, G.1
  • 39
    • 0011690043 scopus 로고
    • Eigenvalue distribution theorems for certain homogeneous spaces
    • H. Widom Eigenvalue distribution theorems for certain homogeneous spaces. Journal of Functional Analysis 32 1979 2 139 147
    • (1979) Journal of Functional Analysis , vol.32 , Issue.2 , pp. 139-147
    • Widom, H.1
  • 40
    • 33748647789 scopus 로고
    • On a class of integral operators with discontinuous symbol
    • Operator Theory: Adv. Appl. Birkhäuser Basel
    • H. Widom On a class of integral operators with discontinuous symbol. Toeplitz Centennial (Tel Aviv, 1981) Operator Theory: Adv. Appl. 4 477 500 Birkhäuser Basel 1982
    • (1982) Toeplitz Centennial (Tel Aviv, 1981) , vol.4 , pp. 477-500
    • Widom, H.1
  • 42
    • 0000142616 scopus 로고
    • On a class of integral operators on a half-space with discontinuous symbol
    • H. Widom On a class of integral operators on a half-space with discontinuous symbol. Journal of Functional Analysis 88 1990 1 166 193
    • (1990) Journal of Functional Analysis , vol.88 , Issue.1 , pp. 166-193
    • Widom, H.1
  • 43
    • 32644460099 scopus 로고    scopus 로고
    • Violation of the entropic area law for fermions
    • 010404 pages
    • M. M. Wolf Violation of the entropic area law for fermions. Physical Review Letters 2006 96 1 010404 4 pages
    • (2006) Physical Review Letters , vol.96 , Issue.1 , pp. 4
    • Wolf, M.M.1
  • 44
    • 4243684526 scopus 로고    scopus 로고
    • Entanglement of formation of an arbitrary state of two qubits
    • W. K. Wootters Entanglement of formation of an arbitrary state of two qubits. Physical Review Letters 1998 80 10 2245 2248
    • (1998) Physical Review Letters , vol.80 , Issue.10 , pp. 2245-2248
    • Wootters, W.K.1


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