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Volumn 2, Issue 1, 2012, Pages 1-18

Entanglement entropy of fermi liquids via multidimensional bosonization

Author keywords

Condensed matter physics; Quantum physics

Indexed keywords

1D CHAIN; BOSONIZATION; COUPLING PARAMETERS; EFFECTIVE HAMILTONIAN; ENTANGLEMENT ENTROPY; FERMION SYSTEMS; FERMIONIC SYSTEMS; HIGH-DIMENSIONAL; HIGHER ORDER; LOGARITHMIC CORRECTIONS; LOW ENERGIES; QUANTUM PHYSICS; SCALING ANALYSIS; SCALING BEHAVIOR; SECOND ORDERS; SPINLESS FERMION; TOY MODELS;

EID: 84863214622     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.2.011012     Document Type: Article
Times cited : (70)

References (45)
  • 2
    • 75849123085 scopus 로고    scopus 로고
    • Entanglement and Magnetic Order
    • 504001
    • L. Amico and R. Fazio, Entanglement and Magnetic Order, J. Phys. A 42, 504001 (2009).
    • (2009) J. Phys. A , vol.42
    • Amico, L.1    Fazio, R.2
  • 3
    • 71049184537 scopus 로고    scopus 로고
    • A Short Review on Entanglement in Quantum Spin Systems
    • 504002
    • J. I. Latorre and A. Riera, A Short Review on Entanglement in Quantum Spin Systems, J. Phys. A 42, 504002 (2009).
    • (2009) J. Phys. A , vol.42
    • Latorre, J.I.1    Riera, A.2
  • 4
    • 77649149203 scopus 로고    scopus 로고
    • Colloquium: Area Laws for the Entanglement Entropy
    • J. Eisert, Colloquium: Area Laws for the Entanglement Entropy, Rev. Mod. Phys. 82, 277 (2010).
    • (2010) Rev. Mod. Phys. , vol.82 , pp. 277
    • Eisert, J.1
  • 5
    • 3442895828 scopus 로고
    • Density Matrix Formulation for Quantum Renormalization Groups
    • S. R. White, Density Matrix Formulation for Quantum Renormalization Groups, Phys. Rev. Lett. 69, 2863 (1992).
    • (1992) Phys. Rev. Lett. , vol.69 , pp. 2863
    • White, S.R.1
  • 6
    • 37649026836 scopus 로고    scopus 로고
    • Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective
    • 227205
    • F. Verstraete, D. Porras, and J. Cirac, Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective, Phys. Rev. Lett. 93, 227205 (2004).
    • (2004) Phys. Rev. Lett. , vol.93
    • Verstraete, F.1    Porras, D.2    Cirac, J.3
  • 8
    • 33645161396 scopus 로고    scopus 로고
    • Detecting Topological Order in a Ground State Wave Function
    • 110405
    • M. Levin and X.-G. Wen, Detecting Topological Order in a Ground State Wave Function, Phys. Rev. Lett. 96, 110405 (2006).
    • (2006) Phys. Rev. Lett. , vol.96
    • Levin, M.1    Wen, X.-G.2
  • 9
    • 33645151438 scopus 로고    scopus 로고
    • Topological Entanglement Entropy
    • 110404
    • A. Kitaev and J. Preskill, Topological Entanglement Entropy, Phys. Rev. Lett. 96, 110404 (2006).
    • (2006) Phys. Rev. Lett. , vol.96
    • Kitaev, A.1    Preskill, J.2
  • 10
    • 46949084674 scopus 로고    scopus 로고
    • Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
    • 010504
    • H. Li and F. D. M. Haldane, Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States, Phys. Rev. Lett. 101, 010504 (2008).
    • (2008) Phys. Rev. Lett. , vol.101
    • Li, H.1    Haldane, F.D.M.2
  • 11
    • 79551610647 scopus 로고    scopus 로고
    • Classification of Gapped Symmetric Phases in One-Dimensional Spin Systems
    • 035107
    • X. Chen, Z.-C. Gu, and X.-G. Wen, Classification of Gapped Symmetric Phases in One-Dimensional Spin Systems, Phys. Rev. B 83, 035107 (2011).
    • (2011) Phys. Rev. B , vol.83
    • Chen, X.1    Gu, Z.-C.2    Wen, X.-G.3
  • 12
    • 0036757880 scopus 로고    scopus 로고
    • Entanglement in a Simple Quantum Phase Transition
    • 032110
    • T. Osborne and M. Nielsen, Entanglement in a Simple Quantum Phase Transition, Phys. Rev. A 66, 032110 (2002).
    • (2002) Phys. Rev. A , vol.66
    • Osborne, T.1    Nielsen, M.2
  • 14
    • 77649149203 scopus 로고    scopus 로고
    • Colloquium: Area Laws for the Entanglement Entropy
    • For a review, see J. Eisert, M. Cramer, and M. B. Plenio, Colloquium: Area Laws for the Entanglement Entropy, Rev. Mod. Phys. 82, 277 (2010).
    • (2010) Rev. Mod. Phys. , vol.82 , pp. 277
    • Eisert, J.1    Cramer, M.2    Plenio, M.B.3
  • 15
    • 2442674839 scopus 로고
    • Geometric and Renormalized Entropy in Conformal Field Theory
    • C. Holzhey, F. Larsen, and F. Wilczek, Geometric and Renormalized Entropy in Conformal Field Theory, Nucl. Phys. B424, 443 (1994).
    • (1994) Nucl. Phys. , vol.B424 , pp. 443
    • Holzhey, C.1    Larsen, F.2    Wilczek, F.3
  • 16
    • 33644887514 scopus 로고    scopus 로고
    • Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture
    • 100503
    • D. Gioev and I. Klich, Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture, Phys. Rev. Lett. 96, 100503 (2006).
    • (2006) Phys. Rev. Lett , vol.96
    • Gioev, D.1    Klich, I.2
  • 17
    • 32644460099 scopus 로고    scopus 로고
    • Violation of the Entropic Area Law for Fermions
    • 010404
    • M.Wolf, Violation of the Entropic Area Law for Fermions, Phys. Rev. Lett. 96, 010404 (2006).
    • (2006) Phys. Rev. Lett. , vol.96
    • Wolf, M.1
  • 18
    • 34547324404 scopus 로고    scopus 로고
    • Statistics Dependence of the Entanglement Entropy
    • 220603
    • M. Cramer, J. Eisert, and M. B. Plenio, Statistics Dependence of the Entanglement Entropy, Phys. Rev. Lett. 98, 220603 (2007).
    • (2007) Phys. Rev. Lett , vol.98
    • Cramer, M.1    Eisert, J.2    Plenio, M.B.3
  • 19
    • 33846881659 scopus 로고    scopus 로고
    • Scaling Behavior of Entanglement in Two- and Three-Dimensional Free-Fermion Systems
    • 073103
    • W. F. Li, L. T. Ding, R. Yu, T. Roscilde, and S. Haas, Scaling Behavior of Entanglement in Two- and Three-Dimensional Free-Fermion Systems, Phys. Rev. B 74, 073103 (2006).
    • (2006) Phys. Rev. B , vol.74
    • Li, W.F.1    Ding, L.T.2    Yu, R.3    Roscilde, T.4    Haas, S.5
  • 20
    • 33748658295 scopus 로고    scopus 로고
    • Entanglement Scaling in Critical Two-Dimensional Fermionic and Bosonic Systems
    • 022329
    • T. Barthel, M.-C. Chung, and U. Schollwöck, Entanglement Scaling in Critical Two-Dimensional Fermionic and Bosonic Systems, Phys. Rev. A 74, 022329 (2006).
    • (2006) Phys. Rev. A , vol.74
    • Barthel, T.1    Chung, M.-C.2    Schollwöck, U.3
  • 21
    • 44349098113 scopus 로고    scopus 로고
    • Zero Dimensional Area Law in a Gapless Fermionic System
    • 205119
    • G. C. Levine and D. J. Miller, Zero Dimensional Area Law in a Gapless Fermionic System, Phys. Rev. B 77, 205119 (2008).
    • (2008) Phys. Rev. B , vol.77
    • Levine, G.C.1    Miller, D.J.2
  • 22
    • 79961206499 scopus 로고    scopus 로고
    • Entanglement Entropy of Critical Spin Liquids
    • 067202
    • Y. Zhang, T. Grover, and A. Vishwanath, Entanglement Entropy of Critical Spin Liquids, Phys. Rev. Lett. 107, 067202 (2011).
    • (2011) Phys. Rev. Lett , vol.107
    • Zhang, Y.1    Grover, T.2    Vishwanath, A.3
  • 23
    • 79953874295 scopus 로고    scopus 로고
    • A Special Case of a Conjecture by Widom with Implications to Fermionic Entanglement Entropy
    • R. Helling, H. Leschke, and W. Spitzer, A Special Case of a Conjecture by Widom with Implications to Fermionic Entanglement Entropy, Int. Math. Res. Not. 2011, 1451 (2011).
    • (2011) Int. Math. Res. Not , vol.2011 , pp. 1451
    • Helling, R.1    Leschke, H.2    Spitzer, W.3
  • 24
    • 84863216237 scopus 로고    scopus 로고
    • A preliminary discussion of this idea, as well as its connection with multidimensional bosonization, was presented earlier by one of us [25]. A similar idea has been independently discussed by B. Swingle [26], based on a gapless mode-counting argument which is equivalent to our toy model. In this present work, we construct the local degrees of freedom explicitly via high-dimensional bosonization, and we use the constructed bosonic theory to compute the entanglement entropy directly. We also generalize the calculation to include Fermi-liquid interaction in a special geometry, which is nontrivial and shows a subleading contribution of approximately O(1)×logL that cannot be accounted for by mode counting
    • A preliminary discussion of this idea, as well as its connection with multidimensional bosonization, was presented earlier by one of us [25]. A similar idea has been independently discussed by B. Swingle [26], based on a gapless mode-counting argument which is equivalent to our toy model. In this present work, we construct the local degrees of freedom explicitly via high-dimensional bosonization, and we use the constructed bosonic theory to compute the entanglement entropy directly. We also generalize the calculation to include Fermi-liquid interaction in a special geometry, which is nontrivial and shows a subleading contribution of approximately O{eth}1{Thorn} _ logL that cannot be accounted for by mode counting.
  • 26
    • 77955151441 scopus 로고    scopus 로고
    • Entanglement Entropy and the Fermi Surface
    • 050502
    • B. Swingle, Entanglement Entropy and the Fermi Surface, Phys. Rev. Lett. 105, 050502 (2010).
    • (2010) Phys. Rev. Lett , vol.105
    • Swingle, B.1
  • 27
    • 84863222632 scopus 로고    scopus 로고
    • Conformal Field Theory on the Fermi Surface
    • 959592; Rényi Entropy, Mutual Information, and Fluctuation Properties of Fermi Liquids
    • B. Swingle, Conformal Field Theory on the Fermi Surface, Phys. Rev. Lett. 105, 959592 (2010); Rényi Entropy, Mutual Information, and Fluctuation Properties of Fermi Liquids.
    • Phys. Rev. Lett , vol.105
    • Swingle, B.1
  • 29
    • 0000313356 scopus 로고
    • Bosonization and Fermion Liquids in Dimensions Greater than One
    • A. Houghton and J. B. Marston, Bosonization and Fermion Liquids in Dimensions Greater than One, Phys. Rev. B 48, 7790 (1993).
    • (1993) Phys. Rev. B , vol.48 , pp. 7790
    • Houghton, A.1    Marston, J.B.2
  • 30
    • 3342969239 scopus 로고
    • Bosonization of the Low Energy Excitations of Fermi Liquids
    • A. Castro Neto and E. Fradkin, Bosonization of the Low Energy Excitations of Fermi Liquids, Phys. Rev. Lett. 72, 1393 (1994).
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 1393
    • Castro Neto, A.1    Fradkin, E.2
  • 31
    • 0000318843 scopus 로고    scopus 로고
    • Bosonization of Fermi Liquids
    • A. Castro Neto and E. Fradkin, Bosonization of Fermi Liquids, Phys. Rev. B 49, 10877 (1994).
    • Phys. Rev. B , vol.49 , pp. 10877
    • Castro Neto, A.1    Fradkin, E.2
  • 32
    • 33748829960 scopus 로고
    • Exact Solution of the Landau Fixed Point via Bosonization
    • A. Castro Neto and E. Fradkin, Exact Solution of the Landau Fixed Point via Bosonization, Phys. Rev. B 51, 4084 (1995).
    • (1995) Phys. Rev. B , vol.51 , pp. 4084
    • Castro Neto, A.1    Fradkin, E.2
  • 33
    • 33748647789 scopus 로고
    • On a Class of Integral Operators with Discontinuous Symbol
    • H. Widom, On a Class of Integral Operators with Discontinuous Symbol, Oper. Th.: Adv. App. 4, 477 (1982).
    • (1982) Oper. Th.: Adv. App. , vol.4 , pp. 477
    • Widom, H.1
  • 34
    • 85192651592 scopus 로고    scopus 로고
    • There is a recently announced proof of Widom's conjecture by A.V. Sobolev, Quasi-Classical Asymptotics for Pseudodifferential Operators with Discontinuous Symbols: Widom's Conjecture
    • There is a recently announced proof of Widom's conjecture by A.V. Sobolev, Quasi-Classical Asymptotics for Pseudodifferential Operators with Discontinuous Symbols: Widom's Conjecture, Funkts. Anal. Prilozh. 44, 313 (2010).
    • (2010) Funkts. Anal. Prilozh. , vol.44 , pp. 313
  • 35
    • 2442560099 scopus 로고    scopus 로고
    • Universality of Entropy Scaling in One Dimensional Gapless Models
    • 096402
    • V. E. Korepin, Universality of Entropy Scaling in One Dimensional Gapless Models, Phys. Rev. Lett. 92, 096402 (2004).
    • (2004) Phys. Rev. Lett. , vol.92
    • Korepin, V.E.1
  • 36
    • 4043058415 scopus 로고    scopus 로고
    • Quantum Spin Chain, Toeplitz Determinants and the Fisher-Hartwig Conjecture
    • B.-Q. Jin and V. E. Korepin, Quantum Spin Chain, Toeplitz Determinants and the Fisher-Hartwig Conjecture, J. Stat. Phys. 116, 79 (2004).
    • (2004) J. Stat. Phys , vol.116 , pp. 79
    • Jin, B.-Q.1    Korepin, V.E.2
  • 37
    • 70450285534 scopus 로고    scopus 로고
    • Entanglement Entropy of Two Disjoint Intervals in Conformal Field Theory
    • P11001
    • P. Calabrese, J. Cardy, and E. Tonni, Entanglement Entropy of Two Disjoint Intervals in Conformal Field Theory, J. Stat. Mech. 11 (2009) P11001.
    • (2009) J. Stat. Mech , vol.11
    • Calabrese, P.1    Cardy, J.2    Tonni, E.3
  • 38
    • 79960256932 scopus 로고    scopus 로고
    • Entanglement Entropy of Two Disjoint Intervals in c = 1 Theories
    • P06012
    • V. Alba, L. Tagliacozzo, and P. Calabrese, Entanglement Entropy of Two Disjoint Intervals in c = 1 Theories, J. Stat. Mech. 06 (2011) P06012.
    • (2011) J. Stat. Mech , vol.6
    • Alba, V.1    Tagliacozzo, L.2    Calabrese, P.3
  • 39
    • 65549152481 scopus 로고    scopus 로고
    • Mutual Information and Boson Radius in a c =1 Critical System in One Dimension
    • 170602
    • S. Furukawa, V. Pasquier, and J. Shiraishi, Mutual Information and Boson Radius in a c = 1 Critical System in One Dimension, Phys. Rev. Lett. 102, 170602 (2009).
    • (2009) Phys. Rev. Lett , vol.102
    • Furukawa, S.1    Pasquier, V.2    Shiraishi, J.3
  • 40
    • 12044253929 scopus 로고
    • Renormalization-Group Approach to Interacting Fermions
    • R. Shankar, Renormalization-Group Approach to Interacting Fermions, Rev. Mod. Phys. 66, 129 (1994).
    • (1994) Rev. Mod. Phys , vol.66 , pp. 129
    • Shankar, R.1
  • 41
    • 84901001853 scopus 로고    scopus 로고
    • Entanglement Entropy and Quantum Field Theory
    • P06002
    • P. Calabrese and J. Cardy, Entanglement Entropy and Quantum Field Theory, J. Stat. Mech. 06 (2004) P06002.
    • (2004) J. Stat. Mech , vol.6
    • Calabrese, P.1    Cardy, J.2
  • 42
    • 79551713223 scopus 로고    scopus 로고
    • Some Calculable Contributions to Entanglement Entropy
    • 050404
    • M. Hertzberg and F. Wilczek, Some Calculable Contributions to Entanglement Entropy, Phys. Rev. Lett. 106, 050404 (2011).
    • (2011) Phys. Rev. Lett , vol.106
    • Hertzberg, M.1    Wilczek, F.2


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