Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2008, Issue 5, 2008, Pages

  Läuchli, Andreas M ^a   Kollath, Corinna ^b  

^a INSTITUT ROMAND DE RECHERCHE NUMÉRIQUE EN PHYSIQUE DES MATÉRIAUX IRRMA   (Switzerland)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

Correlation functions (theory); Density matrix renormalization group calculations; Entanglement in extended quantum systems (theory); Hubbard and related models (theory)

Indexed keywords

EID: 44949151518     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2008/05/P05018     Document Type: Article

References (45)

1. Amico L, Fazio R, Osterloh A and Vedral V 2008 Entanglement in many-body systems Rev. Mod. Phys. 80 517
2. Bloch I, Dalibard J and Zwerger W 2007 Many-body physics with ultracold gases Preprint 0704.3011
3. Lieb E H and Robinson D W 1972 The finite group velocity of quantum spin systems Commun. Math. Phys. 28 251
4. Cramer M, Serafini A and Eisert J 2008 Locality of dynamics in general harmonic quantum systems Preprint 0803.0890
5. Iglói F and Rieger H 2000 Long-range correlations in the nonequilibrium quantum relaxation of a spin chain Phys. Rev. Lett. 85 3233
6. 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
7. Cazalilla M A 2006 Effect of suddenly turning on interactions in the Luttinger model Phys. Rev. Lett. 97 156403
8. Cubitt T S and Cirac J I 2008 Engineering correlation and entanglement dynamics in spin systems Phys. Rev. Lett. 100 180406
9. Cramer M, Dawson C M, Eisert J and Osborne T J 2008 Exact relaxation in a class of nonequilibrium quantum lattice systems Phys. Rev. Lett. 100 030602
10. Calabrese P and Cardy J 2006 Time dependence of correlation functions following a quantum quench Phys. Rev. Lett. 96 136801
11. Calabrese P and Cardy J 2007 Quantum quenches in extended systems J. Stat. Mech. P06008
12. Greiner M, Mandel O, Esslinger T, Hänsch T W and Bloch I 2002 Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms Nature 415 39
13. Holzey C, Larsen F and Wilczek F 1994 Geometric and renormalized entropy in conformal field theory Nucl. Phys. B 424 443
14. Calabrese P and Cardy J 2004 Entanglement entropy and quantum field theory J. Stat. Mech. P06002
15. Kollath C, Läuchli A M and Altman E 2007 Quench dynamics and non-equilibrium phase diagram of the Bose-Hubbard model Phys. Rev. Lett. 98 180601
16. Calabrese P and Cardy J 2005 Evolution of entanglement entropy in one-dimensional systems J. Stat. Mech. P04010
17. Eisert J and Osborne T J 2006 General entanglement scaling laws from time evolution Phys. Rev. Lett. 97 150404
18. 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
19. Jaksch D, Bruder C, Cirac I, Gardiner C W and Zoller P 1998 Cold bosonic atoms in optical lattices Phys. Rev. Lett. 81 3108
20. Zwerger W 2003 Mott-Hubbard transition of cold atoms in optical lattices J. Opt. B: Quantum Semiclass. Opt. 5 S9
21. Fisher M P A, Weichman P B, Grinstein G and Fisher D S 1989 Boson localization and the superfluid-insulator transition Phys. Rev. B 40 546
22. White S R 1992 Density matrix formulation for quantum renormalization groups Phys. Rev. Lett. 69 2863
23. Hallberg K 2006 New trends in density matrix renormalization Adv. Phys. 55 477
24. Schollwock U 2005 The density-matrix renormalization group Rev. Mod. Phys. 77 259
25. Park T J and Light J C 1986 Unitary quantum time evolution by iterative Lanczos reduction J. Chem. Phys. 85 5870
26. Manmana S R, Muramatsu A and Noack R M 2005 Time evolution of one-dimensional quantum many body systems AIP Conf. Proc. 789 269
27. Vidal G 2004 Efficient simulation of one-dimensional quantum many-body systems Phys. Rev. Lett. 93 040502
28. White S R and Feiguin A E 2004 Real time evolution using the density matrix renormalization group Phys. Rev. Lett. 93 076401
29. Daley A J, Kollath C, Schollwöck U and Vidal G 2004 Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces J. Stat. Mech. P04005
30. Affleck I and Ludwig A W W 1991 Universal noninteger 'ground-state degeneracy' in critical quantum systems Phys. Rev. Lett. 67 161
31. Laflorencie N, Sorensen E K, Chang M-S and Affleck I 2006 Boundary effects in the critical scaling of entanglement entropy in 1d systems Phys. Rev. Lett. 96 100603
32. Vidal G, Latorre J I, Rico E and Kitaev A 2003 Entanglement in quantum critical phenomena Phys. Rev. Lett. 90 27902
33. Kühner T D, White S R and Monien H 2000 One-dimensional Bose-Hubbard model with nearest-neighbor interaction Phys. Rev. B 61 12474
34. Zakrzewski J and Delande D 2007 Accurate determination of the superfluid-insulator transition in the one-dimensional Bose-Hubbard model Preprint cond-mat/0701739
35. Buonsante P and Vezzani A 2007 Ground-state fidelity and bipartite entanglement in the Bose-Hubbard model Phys. Rev. Lett. 98 110601
36. Lieb E H 1963 Exact analysis of an interacting Bose gas. II. The excitation spectrum Phys. Rev. 130 1616
37. Kollath C, Schollwöck U, von Delft J and Zwerger W 2005 One-dimensional density waves of ultracold bosons in an optical lattice Phys. Rev. A 71 053606
38. Altman E and Auerbach A 2002 Oscillating superfluidity of bosons in optical lattices Phys. Rev. Lett. 89 250404
39. Huber S D, Altman E, Buchler H P and Blatter G 2007 Dynamical properties of ultracold bosons in an optical lattice Phys. Rev. B 75 085106
40. Cazalilla M A 2004 Are the Tonks regimes in the continuum and on the lattice truly equivalent? Phys. Rev. A 70 041604(R)
41. Groisman B, Popescu S and Winter A 2005 Quantum, classical, and total amount of correlations in a quantum state Phys. Rev. A 72 032317
42. Amico L, Osterloh A, Plastina F, Fazio R and Massimo Palma G M 2004 Dynamics of entanglement in one-dimensional spin systems Phys. Rev. A 69 022304
43. De Chiara G, Montangero S, Calabrese P and Fazio R 2006 Entanglement entropy dynamics in Heisenberg chains J. Stat. Mech. P03001
44. Barmettler P, Rey A M, Demler E, Lukin M D, Bloch I and Gritsev V 2008 Quantum many-body dynamics of coupled double-well superlattices Preprint 0803.1643
45. Wolf M M, Verstraete F, Hastings M B and Cirac J I 2008 Area laws in quantum systems: mutual information and correlations Phys. Rev. Lett. 100 070502