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Volumn 2011, Issue 8, 2011, Pages

Local quantum quenches in critical one-dimensional systems: Entanglement, the Loschmidt echo, and light-cone effects

Author keywords

conformal field theory; entanglement in extended quantum systems (theory); ladders and planes (theory); spin chains

Indexed keywords


EID: 80053531560     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2011/08/P08019     Document Type: Article
Times cited : (186)

References (61)
  • 1
    • 84901001853 scopus 로고    scopus 로고
    • Entanglement entropy and conformal field theory
    • Calabrese P and Cardy J 2004 Entanglement entropy and conformal field theory J. Stat. Mech. P06002
    • (2004) J. Stat. Mech. , vol.2004 , pp. 06002
    • Calabrese, P.1    Cardy, J.2
  • 2
    • 35948964483 scopus 로고    scopus 로고
    • Entanglement and correlation functions following a local quench: A conformal field theory approach
    • Calabrese P and Cardy J 2007 Entanglement and correlation functions following a local quench: a conformal field theory approach J. Stat. Mech. P10004
    • (2007) J. Stat. Mech. , vol.2007 , pp. 10004
    • Calabrese, P.1    Cardy, J.2
  • 3
    • 34548685913 scopus 로고    scopus 로고
    • Evolution of entanglement after a local quench
    • Eisler V and Peschel I 2007 Evolution of entanglement after a local quench J. Stat. Mech. P06005
    • (2007) J. Stat. Mech. , vol.2007 , pp. 06005
    • Eisler, V.1    Peschel, I.2
  • 5
    • 20044389808 scopus 로고
    • Density-matrix algorithms for quantum renormalization groups
    • White S 1993 Density-matrix algorithms for quantum renormalization groups Phys. Rev. B 48 10345
    • (1993) Phys. Rev. , vol.48 , pp. 10345
    • White, S.1
  • 6
    • 23844520141 scopus 로고    scopus 로고
    • The density-matrix renormalization group
    • Schollwöck U 2005 The density-matrix renormalization group Rev. Mod. Phys. 77 259
    • (2005) Rev. Mod. Phys. , vol.77 , pp. 259
    • Schollwöck, U.1
  • 7
    • 42749103810 scopus 로고    scopus 로고
    • Renormalization algorithms for quantum many body systems in two and higher dimensions
    • Verstraete F and Cirac I 2004 Renormalization algorithms for quantum many body systems in two and higher dimensions Phys. Rev. A 70 060302(R)
    • (2004) Phys. Rev. , vol.70 , pp. 060302
    • Verstraete, F.1    Cirac, I.2
  • 8
    • 52149091646 scopus 로고    scopus 로고
    • Class of quantum many-body states that can be efficiently simulated
    • Vidal G 2008 Class of quantum many-body states that can be efficiently simulated Phys. Rev. Lett. 101 110501
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 110501
    • Vidal, G.1
  • 9
    • 33645151438 scopus 로고    scopus 로고
    • Topological entanglement entropy
    • Kitaev A and Preskill J 2006 Topological entanglement entropy Phys. Rev. Lett. 96 110404
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 110404
    • Kitaev, A.1    Preskill, J.2
  • 10
    • 33645161396 scopus 로고    scopus 로고
    • Detecting topological order in a ground state wavefunction
    • Levin M and Wen X-G 2006 Detecting topological order in a ground state wavefunction Phys. Rev. Lett. 96 110405
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 110405
    • Levin, M.1    Wen, X.-G.2
  • 11
    • 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
    • Li H and Haldane F D M 2008 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) Phys. Rev. Lett. , vol.101 , pp. 010504
    • Li, H.1    Haldane, F.D.M.2
  • 12
    • 77649149203 scopus 로고    scopus 로고
    • Area laws for the entanglement entropy - A review
    • Eiser J, Cramer M and Plenio M B 2010 Area laws for the entanglement entropy - a review Rev. Mod. Phys. 82 277
    • (2010) Rev. Mod. Phys. , vol.82 , pp. 277
    • Eiser, J.1    Cramer, M.2    Plenio, M.B.3
  • 14
    • 63149107523 scopus 로고    scopus 로고
    • Quantum noise as an entanglement meter
    • Klich I and Levitov L 2009 Quantum noise as an entanglement meter Phys. Rev. Lett. 102 100502
    • (2009) Phys. Rev. Lett. , vol.102 , pp. 100502
    • Klich, I.1    Levitov, L.2
  • 15
    • 77956526558 scopus 로고    scopus 로고
    • General relation between entanglement and fluctuations in one dimension
    • Song H F, Rachel S and Le Hur K 2010 General relation between entanglement and fluctuations in one dimension Phys. Rev. B 82 012405
    • (2010) Phys. Rev. , vol.82 , pp. 012405
    • Song, H.F.1    Rachel, S.2    Le Hur, K.3
  • 16
    • 79961107937 scopus 로고    scopus 로고
    • Entanglement from charge statistics: Exact relations for many-body systems
    • Song H F, Flindt C, Rachel S, Klich I and Le Hur K 2010 Entanglement from charge statistics: exact relations for many-body systems Phys. Rev. B 83 161408(R)
    • (2010) Phys. Rev. , vol.83 , pp. 161408
    • Song, H.F.1    Flindt, C.2    Rachel, S.3    Klich, I.4    Le Hur, K.5
  • 17
    • 71049168531 scopus 로고    scopus 로고
    • Quantum noise and entanglement generated by a local quench
    • Hsu B, Grosfeld E and Fradkin E 2009 Quantum noise and entanglement generated by a local quench Phys. Rev. B 80 235412
    • (2009) Phys. Rev. , vol.80 , pp. 235412
    • Hsu, B.1    Grosfeld, E.2    Fradkin, E.3
  • 18
    • 79960628644 scopus 로고    scopus 로고
    • Measuring entanglement using quantum quenches
    • Cardy J 2011 Measuring entanglement using quantum quenches Phys. Rev. Lett. 106 150404
    • (2011) Phys. Rev. Lett. , vol.106 , pp. 150404
    • Cardy, J.1
  • 19
    • 79953715692 scopus 로고    scopus 로고
    • Universal behavior of a bipartite fidelity at quantum criticality
    • Dubail J and Stéphan J-M 2011 Universal behavior of a bipartite fidelity at quantum criticality J. Stat. Mech. L03002
    • (2011) J. Stat. Mech. , vol.2011 , pp. 03002
    • Dubail, J.1    Stéphan, J.-M.2
  • 20
    • 29644438531 scopus 로고    scopus 로고
    • Universal adiabatic dynamics in the vicinity of a quantum critical point
    • Polkovnikov A 2005 Universal adiabatic dynamics in the vicinity of a quantum critical point Phys. Rev. B 72 161201(R)
    • (2005) Phys. Rev. , vol.72
    • Polkovnikov, A.1
  • 21
    • 33645521989 scopus 로고    scopus 로고
    • Time dependence of correlation functions following a quantum quench
    • Calabrese P and Cardy J 2006 Time dependence of correlation functions following a quantum quench Phys. Rev. Lett. 96 136801
    • (2006) Phys. Rev. Lett. , vol.96 , pp. 136801
    • Calabrese, P.1    Cardy, J.2
  • 22
    • 36248981522 scopus 로고    scopus 로고
    • Spectroscopy of collective excitations in interacting low-dimensional many-body systems using quench dynamics
    • Gritsev V, Demler E, Lukin M and Polkovnikov A 2007 Spectroscopy of collective excitations in interacting low-dimensional many-body systems using quench dynamics Phys. Rev. Lett. 99 200404
    • (2007) Phys. Rev. Lett. , vol.99 , pp. 200404
    • Gritsev, V.1    Demler, E.2    Lukin, M.3    Polkovnikov, A.4
  • 23
    • 77956314659 scopus 로고    scopus 로고
    • Quench dynamics near a quantum critical point
    • De Grandi C, Gritsev V and Polkovnikov A 2010 Quench dynamics near a quantum critical point Phys. Rev. B 81 012303
    • (2010) Phys. Rev. , vol.81 , pp. 012303
    • De Grandi, C.1    Gritsev, V.2    Polkovnikov, A.3
  • 24
    • 77954791344 scopus 로고    scopus 로고
    • Quench dynamics near a quantum critical point: Application to the sine-Gordon model
    • De Grandi C, Gritsev V and Polkovnikov A 2010 Quench dynamics near a quantum critical point: application to the sine-Gordon model Phys. Rev. B 81 224301
    • (2010) Phys. Rev. , vol.81 , pp. 224301
    • De Grandi, C.1    Gritsev, V.2    Polkovnikov, A.3
  • 26
    • 34548672404 scopus 로고    scopus 로고
    • Quantum quenches in extended systems
    • Calabrese P and Cardy J 2007 Quantum quenches in extended systems J. Stat. Mech. P06008
    • (2007) J. Stat. Mech. , vol.2007 , pp. 06008
    • Calabrese, P.1    Cardy, J.2
  • 27
    • 65549123507 scopus 로고    scopus 로고
    • Inhomogeneous quantum quenches
    • Sotiriadis S and Cardy J 2008 Inhomogeneous quantum quenches J. Stat. Mech. P11003
    • (2008) J. Stat. Mech. , vol.2008 , pp. 11003
    • Sotiriadis, S.1    Cardy, J.2
  • 28
    • 64049095614 scopus 로고    scopus 로고
    • Effective thermal dynamics following a quantum quench in a spin chain
    • Rossini D, Silva A, Mussardo G and Santoro G 2009 Effective thermal dynamics following a quantum quench in a spin chain Phys. Rev. Lett. 102 127204
    • (2009) Phys. Rev. Lett. , vol.102 , pp. 127204
    • Rossini, D.1    Silva, A.2    Mussardo, G.3    Santoro, G.4
  • 29
    • 0037011956 scopus 로고    scopus 로고
    • Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
    • Greiner M, Mandel O, Esslinger T, Hänsch T and Bloch I 2002 Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms Nature 415 39
    • (2002) Nature , vol.415 , pp. 39
    • Greiner, M.1    Mandel, O.2    Esslinger, T.3    Hänsch, T.4    Bloch, I.5
  • 31
    • 4243410292 scopus 로고
    • Chaos and quantum thermalization
    • Srednicki M 1994 Chaos and quantum thermalization Phys. Rev. E 50 888
    • (1994) Phys. Rev. , vol.50 , pp. 888
    • Srednicki, M.1
  • 32
    • 42249112261 scopus 로고    scopus 로고
    • Thermalization and its mechanism for generic isolated quantum systems
    • Rigol M, Dunjko V and Olshanii M 2008 Thermalization and its mechanism for generic isolated quantum systems Nature 452 854
    • (2008) Nature , vol.452 , pp. 854
    • Rigol, M.1    Dunjko, V.2    Olshanii, M.3
  • 33
    • 34247866257 scopus 로고    scopus 로고
    • Quench dynamics and nonequilibrium phase diagram of the Bose-Hubbard model
    • Kollath C, Läuchli A M and Altman E 2007 Quench dynamics and nonequilibrium phase diagram of the Bose-Hubbard model Phys. Rev. Lett. 98 180601
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 180601
    • Kollath, C.1    Läuchli, A.M.2    Altman, E.3
  • 34
    • 76749093169 scopus 로고    scopus 로고
    • Unitary equilibrations: Probability distribution of the Loschmidt echo
    • Campos Venuti L and Zanardi P 2010 Unitary equilibrations: probability distribution of the Loschmidt echo Phys. Rev. A 81 022113
    • (2010) Phys. Rev. , vol.81 , pp. 022113
    • Campos Venuti, L.1    Zanardi, P.2
  • 35
    • 79960643140 scopus 로고    scopus 로고
    • Quantum quench in the transverse-field Ising chain
    • Calabrese P, Essler F H L and Fagotti M 2011 Quantum quench in the transverse-field Ising chain Phys. Rev. Lett. 106 227203
    • (2011) Phys. Rev. Lett. , vol.106 , pp. 227203
    • Calabrese, P.1    Essler, F.H.L.2    Fagotti, M.3
  • 36
    • 2442674839 scopus 로고
    • Geometric and renormalized entropy in conformal field theory
    • Holzhey C, Larsen F and Wilczek F 1994 Geometric and renormalized entropy in conformal field theory Nucl. Phys. B 424 443
    • (1994) Nucl. Phys. , vol.424 , pp. 443
    • Holzhey, C.1    Larsen, F.2    Wilczek, F.3
  • 38
    • 2442560099 scopus 로고    scopus 로고
    • Universality of entropy scaling in one-dimensional gapless models
    • Korepin V 2004 Universality of entropy scaling in one-dimensional gapless models Phys. Rev. Lett. 92 096402
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 096402
    • Korepin, V.1
  • 39
    • 68949145298 scopus 로고    scopus 로고
    • Entanglement entropy with localized and extended interface defects
    • Iglói F, Szatmri Z and Lin Y-C 2009 Entanglement entropy with localized and extended interface defects Phys. Rev. B 80 024405
    • (2009) Phys. Rev. , vol.80 , pp. 024405
    • Iglói, F.1    Szatmri, Z.2    Lin, Y.-C.3
  • 41
    • 38949129854 scopus 로고    scopus 로고
    • Entanglement evolution after connecting finite to infinite quantum chains
    • Eisler V, Karevski D, Platini T and Peschel I 2008 Entanglement evolution after connecting finite to infinite quantum chains J. Stat. Mech. P01023
    • (2008) J. Stat. Mech. , vol.2008 , pp. 01023
    • Eisler, V.1    Karevski, D.2    Platini, T.3    Peschel, I.4
  • 44
    • 33744747026 scopus 로고
    • Conformal invariance, the central charge, and universal finite-size amplitudes at criticality
    • Blöte H W J, Cardy J and Nightingale M P 1986 Conformal invariance, the central charge, and universal finite-size amplitudes at criticality Phys. Rev. Lett. 56 742
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 742
    • Blöte, H.W.J.1    Cardy, J.2    Nightingale, M.P.3
  • 45
    • 0001487832 scopus 로고
    • Universal term in the free energy at a critical point and the conformal anomaly
    • Affleck I 1986 Universal term in the free energy at a critical point and the conformal anomaly Phys. Rev. Lett. 56 746
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 746
    • Affleck, I.1
  • 46
    • 77749345942 scopus 로고    scopus 로고
    • Parity effects in the scaling of block entanglement in gapless spin chains
    • Calabrese P, Campostrini M, Essler F and Nienhuis B 2010 Parity effects in the scaling of block entanglement in gapless spin chains Phys. Rev. Lett. 104 095701
    • (2010) Phys. Rev. Lett. , vol.104 , pp. 095701
    • Calabrese, P.1    Campostrini, M.2    Essler, F.3    Nienhuis, B.4
  • 47
    • 77951786310 scopus 로고    scopus 로고
    • Unusual corrections to scaling in entanglement entropy
    • Cardy J and Calabrese P 2010 Unusual corrections to scaling in entanglement entropy J. Stat. Mech. P04023
    • (2010) J. Stat. Mech. , vol.2010 , pp. 04023
    • Cardy, J.1    Calabrese, P.2
  • 48
    • 79751509192 scopus 로고    scopus 로고
    • Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
    • Fagotti M and Calabrese P 2011 Universal parity effects in the entanglement entropy of XX chains with open boundary conditions J. Stat. Mech. P01017
    • (2011) J. Stat. Mech. , vol.2011 , pp. 01017
    • Fagotti, M.1    Calabrese, P.2
  • 49
    • 33744667096 scopus 로고
    • Effect of boundary conditions on the operator content of two-dimensional conformally invariant theories
    • Cardy J 1986 Effect of boundary conditions on the operator content of two-dimensional conformally invariant theories Nucl. Phys. B 275 200
    • (1986) Nucl. Phys. , vol.275 , pp. 200
    • Cardy, J.1
  • 50
    • 0001560014 scopus 로고
    • Finite-size dependence of the free energy in two-dimensional critical systems
    • Cardy J and Peschel I 1988 Finite-size dependence of the free energy in two-dimensional critical systems Nucl. Phys. B 300 377
    • (1988) Nucl. Phys. , vol.300 , pp. 377
    • Cardy, J.1    Peschel, I.2
  • 51
    • 0031582695 scopus 로고    scopus 로고
    • Fermi edge singularities: Bound states and finite-size effects
    • Zagoskin A M and Affleck I 1997 Fermi edge singularities: bound states and finite-size effects J. Phys. A: Math. Gen. 30 5743
    • (1997) J. Phys. A: Math. Gen. , vol.30 , pp. 5743
    • Zagoskin, A.M.1    Affleck, I.2
  • 52
    • 0001308143 scopus 로고
    • Non-analytic finite-size corrections in the one-dimensional Bose gas and Heisenberg chain
    • Woynarovich F, Eckle H-P and Truong T 1989 Non-analytic finite-size corrections in the one-dimensional Bose gas and Heisenberg chain J. Phys. A: Math. Gen. 22 4027
    • (1989) J. Phys. A: Math. Gen. , vol.22 , pp. 4027
    • Woynarovich, F.1    Eckle, H.-P.2    Truong, T.3
  • 53
    • 0041585485 scopus 로고
    • Non-analytic finite-size corrections for the Heisenberg chain in a magnetic field with free and twisted boundary conditions
    • Eckle H-P and Hamer C 1991 Non-analytic finite-size corrections for the Heisenberg chain in a magnetic field with free and twisted boundary conditions J. Phys. A: Math. Gen. 24 191
    • (1991) J. Phys. A: Math. Gen. , vol.24 , pp. 191
    • Eckle, H.-P.1    Hamer, C.2
  • 54
    • 0011320769 scopus 로고
    • The finite group velocity of quantum spin systems
    • Lieb E and Robinson D 1972 The finite group velocity of quantum spin systems Commun. Math. Phys. 28 251
    • (1972) Commun. Math. Phys. , vol.28 , pp. 251
    • Lieb, E.1    Robinson, D.2
  • 56
    • 77949372290 scopus 로고    scopus 로고
    • Light-cone dynamics and reverse Kibble-Zurek mechanism in two-dimensional superfluids following a quantum quench
    • Mathey I and Polkovnikov A 2010 Light-cone dynamics and reverse Kibble-Zurek mechanism in two-dimensional superfluids following a quantum quench Phys. Rev. A 81 033605
    • (2010) Phys. Rev. , vol.81 , pp. 033605
    • Mathey, I.1    Polkovnikov, A.2
  • 57
    • 47249162387 scopus 로고    scopus 로고
    • Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
    • Fagotti M and Calabrese P 2008 Evolution of entanglement entropy following a quantum quench: analytic results for the XY chain in a transverse magnetic field Phys. Rev. A 78 010306
    • (2008) Phys. Rev. , vol.78 , pp. 010306
    • Fagotti, M.1    Calabrese, P.2
  • 58
    • 65449148310 scopus 로고    scopus 로고
    • Quantum quenches from integrability: The fermionic pairing model
    • Faribault A, Calabrese P and Caux J-S 2009 Quantum quenches from integrability: the fermionic pairing model J. Stat. Mech. P03018
    • (2009) J. Stat. Mech. , vol.2009 , pp. 03018
    • Faribault, A.1    Calabrese, P.2    Caux, J.-S.3
  • 59
    • 70349659829 scopus 로고    scopus 로고
    • Bethe Ansatz approach to quench dynamics in the Richardson model
    • Faribault A, Calabrese P and Caux J-S 2009 Bethe Ansatz approach to quench dynamics in the Richardson model J. Math. Phys. 50 095212
    • (2009) J. Math. Phys. , vol.50 , pp. 095212
    • Faribault, A.1    Calabrese, P.2    Caux, J.-S.3
  • 60
    • 77957588925 scopus 로고    scopus 로고
    • Geometric quenches in quantum integrable systems
    • Mossel J, Palacios G and Caux J-S 2010 Geometric quenches in quantum integrable systems J. Stat. Mech. L09001
    • (2010) J. Stat. Mech. , vol.2010 , pp. 09001
    • Mossel, J.1    Palacios, G.2    Caux, J.-S.3
  • 61
    • 84901050687 scopus 로고    scopus 로고
    • On the reduced density matrix for a chain of free electrons
    • Peschel I 2004 On the reduced density matrix for a chain of free electrons J. Stat. Mech. P06004
    • (2004) J. Stat. Mech. , vol.2004 , pp. 06004
    • Peschel, I.1


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