Universal behavior of a bipartite fidelity at quantum criticality

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2011, Issue 3, 2011, Pages

  Dubail, Jérôme ^a   Stéphan, Jean Marie ^b  

^a Yale University   (United States)

^b DIF   (France)

Author keywords

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

Indexed keywords

EID: 79953715692     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2011/03/L03002     Document Type: Article

References (40)

1. Amico L, Fazio R, Osterloh A and Vedral V 2008 Entanglement in many-body systems Rev. Mod. Phys. 80 517
2. Calabrese P, Cardy J and Doyon B 2009 Entanglement entropy in extended quantum systems J. Phys. A: Math. Theor. 42 500301
3. Eisert J, Cramer M and Plenio M B 2010 Colloquium: area laws for the entanglement entropy Rev. Mod. Phys. 82 277
4. Holzey C, Larsen F and Wilczek F 1994 Geometric and renormalized entropy in conformal field theory Nucl. Phys. B 424 443
5. Vidal G, Latorre J I, Rico E and Kitaev A 2003 Entanglement in quantum critical phenomena Phys. Rev. Lett. 90 227902
6. Calabrese P and Cardy J 2004 Entanglement entropy and quantum field theory J. Stat. Mech. P06002
7. Wolf M 2006 Violation of the entropic area law for fermions Phys. Rev. Lett. 96 010404
8. Gioev D and Klich I 2006 Entanglement entropy of fermions in any dimension and the Widom conjecture Phys. Rev. Lett. 96 100503
9. Kitaev A and Preskill J 2006 Topological entanglement entropy Phys. Rev. Lett. 96 110404
10. Levin M and Wen X-G 2006 Detecting topological order in a ground state wavefunction Phys. Rev. Lett. 96 110405
11. Hamma A, Ionicioiu R and Zanardi P 2005 Ground state entanglement and geometric entropy in the Kitaev model Phys. Lett. A 337 22
12. Fradkin E and Moore J E 2006 Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum Phys. Rev. Lett. 97 050404
13. Haque M, Zozulya O and Schoutens K 2007 Entanglement entropy in fermionic Laughlin states Phys. Rev. Lett. 98 060401
14. Metlitski M A, Fuertes C A and Sachdev S 2009 Entanglement entropy in the O(N) model Phys. Rev. B 80 115122
15. Stéphan J-M, Furukawa S, Misguich G and Pasquier V 2009 Shannon and entanglement entropies of one- and two-dimensional critical wavefunctions Phys. Rev. B 79 115421
16. Stéphan J-M, Misguich G and Pasquier V 2010 Rényi entropy of a line in two-dimensional Ising models Phys. Rev. B 82 125455
17. Oshikawa M 2010 arXiv:1007:3729
18. Anderson P W 1967 Infrared catastrophe in Fermi gases with local scattering potentials Phys. Rev. Lett. 18 1049
19. Zanardi P and Paunković N 2006 Ground state overlap and quantum phase transitions Phys. Rev. E 74 031123
20. Sirker J 2010 Finite-temperature fidelity susceptibility for one-dimensional quantum systems Phys. Rev. Lett. 105 117203
21. Gu S-J 2010 Fidelity approach to quantum phase transitions Int. J. Mod. Phys. B 24 4371
22. Campos Venuti L, Saleur H and Zanardi P 2009 Universal subleading terms in ground-state fidelity from boundary conformal field theory Phys. Rev. B 79 092405
23. Schwandt D, Alet F and Capponi S 2009 Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions Phys. Rev. Lett. 103 170501
24. Peres A 1984 Stability of quantum motion in chaotic and regular systems Phys. Rev. A 30 1610
25. Gorin T, Prosen T, Seligman T and Znidaric M 2006 Dynamics of Loschmidt echoes and fidelity decay Phys. Rep. 435 33
26. Pastawski H M, Levstein P R, Usaj G, Raya J and Hirschinger J 2000 A nuclear magnetic resonance answer to the Boltzmann-Loschmidt controversy? Physica A 283 166
27. Jalabert R A and Pastawski H M 2001 Environment-independent decoherence rate in classically chaotic systems Phys. Rev. Lett. 86 2490
28. Quan H T, Song Z, Liu X F, Zanardi P and Sun C P 2006 Decay of Loschmidt echo enhanced by quantum criticality Phys. Rev. Lett. 96 140604
29. Campos Venuti L and Zanardi P 2010 Universal equilibrium distribution after a small quantum quench Phys. Rev. A 81 022113
30. Di Francesco P, Matthieu P and Sénéchal D 1997 Conformal Field Theory (Berlin: Springer)
31. Dubail J, Stéphan J-M and Pasquier V unpublished notes
32. Cardy J and Peschel I 1988 Finite-size dependence of the free energy in two-dimensional critical systems Nucl. Phys. B 300 377
33. Iglói F and Juhsz R 2008 Exact relationship between the entanglement entropies of XY and quantum Ising chains Europhys. Lett. 81 57003
34. Calabrese P and Cardy J 2007 Entanglement and correlation functions following a local quench: a conformal field theory approach J. Stat. Mech. P10004
35. Klich I and Levitov L 2009 Quantum noise as an entanglement meter Phys. Rev. Lett. 102 100502
36. Song H F, Rachel S and Le Hur K 2010 General relation between entanglement and fluctuations in one dimension Phys. Rev. 82 012405
37. Song H F, Flindt C, Rachel S, Klich I and Le Hur K 2010 arXiv:1008.5191
38. Alet F, Jacobsen J L, Misguich G, Pasquier V, Mila F and Troyer M 2005 Interacting classical dimers on the square lattice Phys. Rev. Lett. 94 235702
39. Affleck I and Ludwig A 1991 Universal noninteger ground-state degeneracy in critical quantum systems Phys. Rev. Lett. 67 161
40. Fendley P, Saleur H and Warner N P 1994 Exact solution of a massless scalar field with a relevant boundary condition Nucl. Phys. B 430 577