Scaling of rényi entanglement entropies of the free fermi-gas ground state: A rigorous proof

Physical Review Letters

Volumn 112, Issue 16, 2014, Pages

  Leschke, Hajo ^a,b   Sobolev, Alexander V ^c   Spitzer, Wolfgang ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b UNIVERSITY OF HAGEN   (Germany)

^c UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; MATHEMATICAL OPERATORS;

ASYMPTOTIC GROWTH; ENTANGLEMENT ENTROPY; EUCLIDEAN SPACES; FUNCTIONAL CALCULUS; LOGARITHMIC NEGATIVITY; NONINTERACTING FERMIONS; PSEUDO-DIFFERENTIAL OPERATOR; ZERO TEMPERATURES;

QUANTUM ENTANGLEMENT;

EID: 84899561574     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.112.160403     Document Type: Article

References (42)

1. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000);
2. M. Hayashi, Quantum Information: An Introduction (Springer-Verlag, Berlin, 2006);
3. J. Audretsch, Entangled Systems (Wiley-VCH, Berlin, 2007);
4. J. Stolze and D. Suter, Quantum Computing: A Short Course from Theory to Experiment (Wiley-VCH, Weinheim, 2008), 2nd ed.
5. J. Eisert, M. Cramer, and M.B. Plenio, Rev. Mod. Phys. 82, 277 (2010). RMPHAT 0034-6861 10.1103/RevModPhys.82.277
6. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008); RMPHAT 0034-6861 10.1103/RevModPhys.80.517 (Pubitemid 351697445)
7. I. Peschel, Braz. J. Phys. 42, 267 (2012). BJPHE6 0103-9733 10.1007/s13538-012-0074-1
8. L. Bombelli, R.K. Koul, J.-H. Lee, and R.D. Sorkin, Phys. Rev. D 34, 373 (1986); PRVDAQ 0556-2821 10.1103/PhysRevD.34.373
9. M. Srednicki, Phys. Rev. Lett. 71, 666 (1993). PRLTAO 0031-9007 10.1103/PhysRevLett.71.666
10. M. Fannes, B. Nachtergaele, and R.F. Werner, Commun. Math. Phys. 144, 443 (1992). CMPHAY 0010-3616 10.1007/BF02099178
11. S.R. White, Phys. Rev. Lett. 69, 2863 (1992); PRLTAO 0031-9007 10.1103/PhysRevLett.69.2863
12. U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005); RMPHAT 0034-6861 10.1103/RevModPhys.77.259 (Pubitemid 41490660)
13. M.B. Hastings, Phys. Rev. B 76, 035114 (2007). PRBMDO 1098-0121 10.1103/PhysRevB.76.035114
14. G. Vidal, J.I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003); PRLTAO 0031-9007 10.1103/PhysRevLett.90.227902
15. M. Fannes, B. Haegeman, and M. Mosonyi, J. Math. Phys. 44, 6005 (2003); JMAPAQ 0022-2488 10.1063/1.1623616 (Pubitemid 37514280)
16. V.E. Korepin, Phys. Rev. Lett. 92, 096402 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.096402
17. B.-Q. Jin and V.E. Korepin, J. Stat. Phys. 116, 79 (2004). JSTPBS 0022-4715 10.1023/B:JOSS.0000037230.37166.42 (Pubitemid 39129772)
18. M.M. Wolf, Phys. Rev. Lett. 96, 010404 (2006); PRLTAO 0031-9007 10.1103/PhysRevLett.96.010404 (Pubitemid 43248320)
19. D. Gioev, Int. Math. Res. Not. 2006, 95181 (2006). 1073-7928
20. D. Gioev and I. Klich, Phys. Rev. Lett. 96, 100503 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.100503
21. T. Barthel, M. -C. Chung, and U. Schollwöck, Phys. Rev. A 74, 022329 (2006); PLRAAN 1050-2947 10.1103/PhysRevA.74.022329 (Pubitemid 44385012)
22. W. Li, L. Ding, R. Yu, T. Roscilde, and S. Haas, Phys. Rev. B 74, 073103 (2006); PRBMDO 1098-0121 10.1103/PhysRevB.74.073103
23. S. Farkas and Z. Zimboras, J. Math. Phys. (N.Y.) 48, 102110 (2007). JMAPAQ 0022-2488 10.1063/1.2800167
24. R. Helling, H. Leschke, and W. Spitzer, Int. Math. Res. Not. 2011, 1451 (2011). 1073-7928
25. B. Swingle, Phys. Rev. Lett. 105, 050502 (2010); PRLTAO 0031-9007 10.1103/PhysRevLett.105.050502
26. P. Calabrese, M. Mintchev, and E. Vicari, Phys. Rev. Lett. 107, 020601 (2011); PRLTAO 0031-9007 10.1103/PhysRevLett.107.020601
27. W. Ding, A. Seidel, and K. Yang, Phys. Rev. X 2, 011012 (2012). PRXHAE 2160-3308 10.1103/PhysRevX.2.011012
28. P. Calabrese, M. Mintchev, and E. Vicari, Europhys. Lett. 97, 20009 (2012); EULEEJ 0295-5075 10.1209/0295-5075/97/20009
29. P. Calabrese, M. Mintchev, and E. Vicari, Europhys. Lett. 98, 20003 (2012); EULEEJ 0295-5075 10.1209/0295-5075/98/20003
30. B. Swingle, Phys. Rev. B 86, 045109 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.045109
31. B. Swingle, Phys. Rev. B 86, 035116 (2012). PRBMDO 1098-0121 10.1103/PhysRevB.86.035116
32. R. Balian, From Microphysics to Macrophysics (Springer-Verlag, Berlin, 1992), Vol. II.
33. A.V. Sobolev, arXiv:1312.1835.
34. G. Vidal and R.F. Werner, Phys. Rev. A 65, 032314 (2002). PLRAAN 1050-2947 10.1103/PhysRevA.65.032314
35. R.J. Gardner, Geometric Tomography (Cambridge University Press, Cambridge, England, 2006), 2nd ed.
36. A.V. Sobolev, arXiv:1310.2083, [J. Funct. Anal. (to be published)].
37. H.J. Landau and H. Widom, J. Math. Anal. Appl. 77, 469 (1980). JMANAK 0022-247X 10.1016/0022-247X(80)90241-3
38. A.V. Sobolev, Mem. Am. Math. Soc. 222, 1043 (2013). MAMCAU 0065-9266 10.1090/S0065-9266-2012-00670-8
39. H. Widom, Oper. Theory Adv. Appl. 4, 477 (1982).
40. A proof of the Widom conjecture in the special case with a quadratic (Equation presented) was announced in Ref. [10] and given in Ref. [12].
41. B. Simon, Trace Ideals and Their Applications (American Mathematical Society, Providence, RI, 2005), 2nd ed;
42. M.S. Birman and M.Z. Solomyak, Spectral Theory of Self-Adjoint Operators in Hilbert Space (D. Reidel Publishing Company, Dordrecht, Holland, 1987).