Asymptotics of Toeplitz determinants and the emptiness formation probability for the XY spin chain

Journal of Physics A: Mathematical and General

Volumn 38, Issue 23, 2005, Pages 5069-5095

  Franchini, Fabio ^a   Abanov, Alexander G ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 19944408980     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/23/002     Document Type: Article

References (39)

1. Bethe H 1931 Zur Theorie der Metalle: I. Eingenwerte and Eigenfunktionen der linearen Atomkette Z. Phys. 71 205
2. Yang C N and Yang C P 1966 One-dimensional chain of anisotropic spin-spin interactions: II. Properties of the ground-state energy per lattice site for an infinite system Phys. Rev. 150 327
3. Korepin V E, Bogoliubov N M and Izergin A G 1993 Quantum Inverse Scattering Method and Correlation Functions (Cambridge: Cambridge University Press)
4. Jimbo M and Miwa T 1995 Algebraic Analysis of Solvable Lattice Models no 85 (Providence, RI: American Mathematical Society)
5. Korepin V E, Izergin A G, Essler F H L and Uglov D B 1994 Correlation functions of the spin-1/2 XXX antiferromagnet Phys. Lett. A 190 182
6. Abanov A G and Korepin V E 2002 On the probability of ferromagnetic strings in antiferromagnetic spin chains Nucl. Phys. B 647 565
7. Shiroishi M, Takahashi M and Nishiyama Y 2001 Emptiness formation probability for the one-dimensional isotropic XY model J. Phys. Soc. Japan 70 3535
8. Boos H E, Korepin V E, Nishiyama Y and Shiroishi M 2002 Quantum correlations and number theory J. Phys. A: Math. Gen. 35 4443
9. Yu Stroganov 2001 The importance of being odd J. Phys. A: Math. Gen. 34 L179
10. Razumov A V Yu and Stroganov G 2001 Spin chains and combinatorics J. Phys. A: Math. Gen. 34 3185
11. Kitanine N, Maillet J M, Slavnov N A and Terras V 2002 Correlation functions of the XXZ spin- Heisenberg chain at free fermion point from their multiple integral representations J. Nucl. Phys. B 642 433-55
12. Kitanine N, Maillet J M, Slavnov N A and Terras V 2002 Emptiness formation probability of the XXZ spin- Heisenberg chain at J. Phys. A: Math. Gen. 35 L385-8
13. Kitanine N, Maillet J M, Slavnov N A and Terras V 2002 Large distance asymptotic behaviour of the emptiness formation probability of the XXZ spin- Heisenberg chain J. Phys. A: Math. Gen. 35 L753-8
14. Korepin V E, Lukyanov S, Nishiyama Y and Shiroishi M 2003 Asymptotic behavior of the emptiness formation probability in the critical phase of XXZ spin chain Phys. Lett. A 312 21
15. Barouch E, McCoy B M and Dresden M 1970 Statistical mechanics of the XY model: I Phys. Rev. A 2 1075
16. Barouch E and McCoy B M 1971 Statistical mechanics of the XY model: II. Spin-correlation functions Phys. Rev. A 3 786
17. Barouch E and McCoy B M 1971 Statistical mechanics of the XY model: III Phys. Rev. A 3 2137
18. McCoy B M, Barouch E and Abraham D B 1971 Statistical mechanics of the XY model: IV. Time-dependent spin-correlation functions Phys. Rev. A 4 2331
19. Abanov A G and Franchini F 2003 Emptiness formation probability for the anisotropic XY spin chain in a magnetic field Phys. Lett. A 316 342
20. Lieb E, Schultz T and Mattis D 1961 Two soluble models of an antiferromagnetic chain Ann. Phys. 16 407-66
21. Mehta K L 1977 Matrix Theory-Selected Topics and Useful Results (Les Ulis: Les Editions de Physique)
22. Kurmann J, Thomas H and Müller G 1982 Antiferromagnetic long-range order in the anisotropic quantum spin chain Physica A 112 235
23. Müller G and Shrock R E 1985 Implications of direct-product ground states in the one-dimensional quantum XYZ and XY spin chains Phys. Rev. B 32 5845
24. des Cloizeaux J and Mehta M L 1973 Asymptotic behavior of spacing distributions for eigenvalues of random matrices J. Math. Phys. 14 1648
25. Dyson F 1976 Fredholm determinants and inverse scattering problems Commun. Math. Phys. 47 171
26. Basor E L and Morrison K E 1994 The Fisher-Hartwig conjecture and Toeplitz eigenvalues Lin. Alg. Appl. 202 129
27. Basor E L and Tracy C A 1991 The Fisher-Hartwig conjecture and generalizations Physica A 177 167
28. Jin B-Q and Korepin V E 2004 Entanglement, Toeplitz determinants and Fisher-Hartwig conjecture J. Stat. Phys. 116 79-95
29. Its A R, Jin B-Q and Korepin V E 2004 Entanglement in XY spin chain Preprint quant-ph/0409027
30. Keating J P and Mezzadri F 2004 Random matrix theory and entanglement in quantum spin chains Commun. Math. Phys. 252 543
31. Ehrhardt T and Th Operator 2001 A status report on the asymptotic behaviour of Toeplitz determinants with Fisher-Hartwig singularities Adv. Appl. 124 217-41
32. Hirschman Jr I I 1966 The strong Szegö limit theorem for Toeplitz determinants Am. J. Math. 88 577
33. McCoy B M and Wu T T 1973 The Two Dimensional Ising Model (Cambridge, MA: Harvard University Press)
34. Fisher M E R E 1968 Hartwig Toeplitz determinants, some applications, theorems and conjectures Adv. Chem. Phys. 15 333
35. Widom H 1973 Toeplitz determinants with singular generating functions Am. J. Math. 95 333
36. Ehrhardt T and Silbermann B 1997 Toeplitz determinants with one Fisher-Hartwig singularity J. Funct. Anal. 148 229-56
37. Widom H 1971 The strong Szegö limit theorem for circular arcs Ind. Univ. Math. J. 21 277
38. Toda M, Kubo R and Saito N 1992 Statistical Physics vol 2 (New York: Springer)
39. Muskhelishvili N I 1953 Singular Integral Equations and Boundary Problems (Groningen: Noordhoff)