Quantum quenches in extended systems

Journal of Statistical Mechanics: Theory and Experiment

Volumn , Issue 6, 2007, Pages

  Calabrese, Pasquale ^a,b   Cardy, John ^c,d  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

^c UNIVERSITY OF OXFORD   (United Kingdom)

^d ALL SOULS COLLEGE   (United Kingdom)

Author keywords

Conformal field theory (theory); Correlation functions; Quantum phase transitions (theory)

Indexed keywords

EID: 34548672404     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2007/06/P06008     Document Type: Article

References (75)

1. Greiner M, Mandel O, Hänsch T W and Bloch I 2002 Collapse and revival of the matter wave field of a Bose-Einstein condensate Nature 419 51 [cond-mat/0207196]
2. Sadler L E, Higbie J M, Leslie S R, Vengalattore M and Stamper-Kurn D M 2006 Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose-Einstein condensate Nature 443 312
3. Lamacraft A 2006 Quantum quenches in a spinor condensate Phys. Rev. Lett. 98 160404 [cond-mat/0611017]
4. Paredes B, Widera A, Murg V, Mandel O, Falling S, Cirac I, Shlyapnikov G V, Hansch T W and Bloch I 2004 Tonks-Girardeau gas of ultracold atoms in an optical lattice Nature 429 277
5. Kinoshita T, Wenger T and Weiss D S 2004 Observation of a one-dimensional Tonks-Girardeau gas Science 305 1125
6. Kinoshita T, Wenger T and Weiss D S 2006 A quantum Newton's cradle Nature 440 900
7. Orzel C, Tuchman A K, Fenselau M L, Yasuda M and Kasevich M A 2001 Squeezed states in a Bose-Einstein condensate Science 291 2386
8. Widera A, Gerbier F, Fölling S, Gericke T, Mandel O and Bloch I 2005 Coherent collisional spin dynamics in optical lattices Phys. Rev. Lett. 95 190405
9. Cazalilla M A and Marston J B 2002 Time-dependent density-matrix renormalization group: a systematic method for the study of quantum many-body systems out-of-equilibrium Phys. Rev. Lett. 88 256403 [cond-mat/0109158]
10. Luo H G, Xiang T and Wang X Q 2003 Comment on 'time-dependent density-matrix renormalization group: a systematic method for the study of quantum many-body out-of-equilibrium systems' Phys. Rev. Lett. 91 049701 [cond-mat/0212580]
11. Vidal G 2004 Efficient simulation of one-dimensional quantum many-body systems Phys. Rev. Lett. 93 040502 [quant-ph/0310089]
12. Daley A J, Kollath C, Schollwoeck U and Vidal G 2004 Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces J. Stat. Mech. P04005 [cond-mat/0403313]
13. White S R and Feiguin A E 2004 Real time evolution using the density matrix renormalization group Phys. Rev. Lett. 93 076401 [cond-mat/0403310]
14. Verstraete F, Garcia-Ripoll J J and Cirac J I 2004 Matrix product density operators: simulation of finite-T and dissipative systems Phys. Rev. Lett. 93 207204 [cond-mat/0406426]
15. Gobert D, Kollath C, Schollwoeck U and Schuetz G 2005 Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG Phys. Rev. E 71 036102 [cond-mat/0409692]
16. Barouch E and McCoy B 1970 Statistical mechanics of the XY model. I Phys. Rev. A 2 1075
17. Barouch E and McCoy B 1971 Statistical mechanics of the XY model. II. Spin-correlation functions Phys. Rev. A 3 786
18. Barouch E and McCoy B 1971 Statistical mechanics of the XY model. III Phys. Rev. A 3 2137
19. Igloi F and Rieger H 2000 Long-range correlations in the nonequilibrium quantum relaxation of a spin chain Phys. Rev. Lett. 85 3233 [cond-mat/0003193]
20. Amico L and Osterloh A 2004 Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations J. Phys. A: Math. Gen. 37 291 [cond-mat/0306285]
21. Sengupta K, Powell S and Sachdev S 2004 Quench dynamics across quantum critical points Phys. Rev. A 69 053616 [cond-mat/0311355]
22. Cherng R W and Levitov L S 2006 Entropy and correlation functions of a driven quantum spin chain Phys. Rev. A 73 043614 [cond-mat/0512689]
23. Das A, Sengupta K, Sen D and Chakrabarti B K 2006 Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point Phys. Rev. B 74 144423 [cond-mat/0606137]
24. Cubitt T S and Cirac J I 2007 Engineering correlation and entanglement dynamics in spin systems Preprint quant-ph/0701053
25. Rigol M, Dunjko V, Yurovsky V and Olshanii M 2007 Relaxation in a completely integrable many-body quantum system: an ab initio study of the dynamics of the highly excited states of lattice hard-core bosons Phys. Rev. Lett. 98 50405 [cond-mat/0604476]
26. del Campo A and Muga J G 2006 Dynamics of a Tonks-Girardeau gas released from a hard-wall trap Europhys. Lett. 74 965 [cond-mat/0511747]
27. Ruschhaupt A, del Campo A and Muga J G 2006 Momentum interferences of a freely expanding Bose-Einstein condensate in 1D due to interatomic interaction change Eur. Phys. J. D 40 399 [cond-mat/0601437]
28. Rodriguez K, Manmana S R, Rigol M, Noack R M and Muramatsu A 2006 Coherent matter waves emerging from Mott-insulators New J. Phys. 8 169 [cond-mat/0606155]
29. Rigol M, Muramatsu A and Olshanii M 2006 Hard-core bosons on optical superlattices: dynamics and relaxation in the superfluid and insulating regimes Phys. Rev. A 74 053616 [cond-mat/0612415]
30. Tuchman A K, Orzel C, Polkovnikov A and Kasevich M A 2005 Non-equilibrium coherence dynamics of a soft boson lattice Preprint cond-mat/0504762
31. Berman G P, Borgonovi F, Izrailev F M and Smerzi A 2004 Irregular dynamics in a one-dimensional Bose system Phys. Rev. Lett. 92 030404 [cond-mat/0309459]
32. Minguzzi A and Gangardt D M 2005 Exact coherent states of a harmonically confined Tonks-Girardeau gas Phys. Rev. Lett. 94 240404 [cond-mat/0504024]
33. Kollath C, Schollwoeck U, von Delft J and Zwerger W 2005 One-dimensional density waves of ultracold bosons in an optical lattice Phys. Rev. A 71 053606 [cond-mat/0411403]
34. Kollath C, Laeuchli A and Altman E 2007 Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model Phys. Rev. Lett. 98 180601 [cond-mat/0607235]
35. Cramer M, Dawson C M, Eisert J and Osborne T J 2007 Quenching, relaxation, and a central limit theorem for quantum lattice systems Preprint cond-mat/0703314
36. Altman E and Auerbach A 2002 Oscillating superfluidity of Bosons in optical lattices Phys. Rev. Lett. 89 250404 [cond-mat/0206157]
37. Cazalilla M A 2006 Effect of suddenly turning on the interactions in the Luttinger model Phys. Rev. Lett. 97 156403 [cond-mat/0606236]
38. Perfetto E 2006 Time-dependent evolution of two coupled Luttinger liquids Phys. Rev. B 74 205123 [cond-mat/0607720]
39. Gritsev V, Demler E, Lukin M and Polkovnikov A 2007 Analysis of quench dynamics of coupled one dimensional condensates using quantum sine Gordon model Preprint cond-mat/0702343
40. Manmana S R, Wessel S, Noack R M and Muramatsu A 2007 Strongly correlated fermions after a quantum quench Phys. Rev. Lett. 98 210405 [cond-mat/0612030]
41. Yuzbashyan E A, Altshuler B L, Kuznetsov V B and Enolskii V Z 2005 Nonequilibrium Cooper pairing in the nonadiabatic regime Phys. Rev. B 72 220503(R) [cond-mat/0505493]
42. Yuzbashyan E A, Tsyplyatyev O and Altshuler B L 2006 Relaxation and persistent oscillations of the order parameter in fermionic condensate Phys. Rev. Lett. 96 097005
43. Barankov R A and Levitov L S 2006 Synchronization in the BCS pairing dynamics as a critical phenomenon Phys. Rev. Lett. 96 230403 [cond-mat/0603317]
44. Yuzbashyan E A and Dzero M 2006 Dynamical vanishing of the order parameter in a fermionic condensate Phys. Rev. Lett. 96 230404 [cond-mat/0603404]
45. Altman E and Vishwanath A 2005 Dynamic projection on Feshbach molecules: a probe of pairing and phase fluctuations Phys. Rev. Lett. 95 110404 [cond-mat/0501683]
46. Barankov R A and Levitov L S 2005 Dynamical projection of atoms to Feshbach molecules at strong coupling Preprint cond-mat/0506323
47. Zurek W H, Dorner U and Zoller P 2005 Dynamics of a quantum phase transition Phys. Rev. Lett. 95 105701 [cond-mat/0503511]
48. Polkovnikov A 2005 Universal adiabatic dynamics across a quantum critical point Phys. Rev. B 72 161201(R) [cond-mat/0312144]
49. Dziarmaga J 2006 Dynamics of a quantum phase transition in the random Ising model Phys. Rev. B 74 64416 [cond-mat/0603814]
50. Cincio L, Dziarmaga J, Rams M M and Zurek W H 2007 Entropy of entanglement and correlations induced by a quench: dynamics of a quantum phase transition in the quantum Ising model Phys. Rev. A 75 052321 [cond-mat/0701768]
51. Calabrese P and Cardy J 2006 Phys. Rev. Lett. 96 136801 [cond-mat/0601225]
52. Diehl H W 1986 The theory of boundary critical phenomena Phase Transitions and Critical Phenomena vol 10 ed C Domb and J L Lebowitz (London: Academic)
53. Diehl H W 1997 The theory of boundary critical phenomena Int. J. Mod. Phys. B 11 3503 [cond-mat/9610143]
54. Cardy J L 1984 Conformal invariance and surface critical behaviour Nucl. Phys. B 240 514
55. Cardy J L 2006 Boundary conformal field theory Encyclopedia of Mathematical Physics ed J-P Francoise, G Naber and S Tsun Tsou (Amsterdam: Elsevier)
56. Cardy J and Lewellen D 1991 Bulk and boundary operators in conformal field theory Phys. Lett. B 259 274
57. Blöte H, Cardy J and Nightingale P 1986 Conformal invariance, the central charge, and universal finite size amplitudes at criticality Phys. Rev. Lett. 56 742
58. Calabrese P and Cardy J 2005 Evolution of entanglement entropy in one dimensional systems J. Stat. Mech. P04010 [cond-mat/0503393]
59. Calabrese P and Cardy J 2004 Entanglement entropy and quantum field theory J. Stat. Mech. P06002 [hep-th/0405152]
60. De Chiara G, Montangero S, Calabrese P and Fazio R 2006 Entanglement entropy dynamics in Heisenberg chains J. Stat. Mech. P03001 [cond-mat/0512586]
61. http://functions.wolfram.com/HypergeometricFunctions/MeijerG1/
62. Klimpel R and Dietrich S 1999 Structure factor of thin films near continuous phase transitions Phys. Rev. B 60 16977
63. Krech M, Eisenriegler E and Dietrich S 1995 Energy density profiles in critical films Phys. Rev. E 52 1345
64. Krech M 1997 Casimir force in binary liquid mixtures Phys. Rev. E 56 1642 and references therein
65. Borjan Z and Upton P J 1998 Order parameter profiles and Casimir amplitudes in critical slabs Phys. Rev. Lett. 81 4911
66. Eisert J and Osborne T J 2006 General entanglement scaling laws from time evolution Phys. Rev. Lett. 97 150404 [quant-ph/0603114]
67. Bravyi S, Hastings M B and Verstraete F 2006 Lieb-Robinson bounds and the generation of correlations and topological quantum order Phys. Rev. Lett. 97 050401 [quant-ph/0603121]
68. Sotiriadis S and Cardy J 2007 in progress
69. Burrell C K and Osborne T J 2007 Bounds on information propagation in disordered quantum spin chains Preprint quant-ph/0703209
70. Anderson P W 1959 Absence of diffusion in certain random lattices Phys. Rev. 109 1492
71. Igloi F and Monthus C 2005 Strong disorder RG approach of random systems Phys. Rep. 412 277 [cond-mat/0502448]
72. Amico L, Osterloh A, Plastina F, Fazio R and Palma G M 2004 Dynamics of entanglement in one-dimensional spin systems Phys. Rev. A 69 022304 [quant-ph/0307048]
73. Kollath C, Schollwoeck U and Zwerger W 2005 Spin-charge separation in cold Fermi-gases: a real time analysis Phys. Rev. Lett. 95 176401 [cond-mat/0504299]
74. Eisler V and Peschel I 2007 Evolution of entanglement after a local quench Preprint cond-mat/0703379
75. Saleur H 1998 Lectures on non perturbative field theory and quantum impurity problems Preprint cond-mat/9812110