Emptiness formation probability, Toeplitz determinants, and conformal field theory
作者： Jean-Marie Stéphan
DOI: 10.1088/1742-5468/2014/05/P05010
关键词:
摘要: We revisit the study of emptiness formation probability, probability forming a sequence $\ell$ spins with same ferromagnetic orientation in ground-state quantum spin chain. focus on two different examples, exhibiting strikingly behavior: XXZ and Ising chains. One has conserved number particles, other does not. In latter we show that fixed can be viewed as an additional boundary imaginary time. then use conformal field theory (CFT) techniques to derive all universal terms its scaling, provide checks free fermionic systems. These are based numerical simulations or, when possible, mathematical results asymptotic behavior Toeplitz Toeplitz+Hankel determinants. A perturbed CFT analysis uncovers interesting $\ell^{-1}\log \ell$ correction, also appears closely related full counting statistics. The case turns out more challenging, scale invariance is broken. simple qualitative picture which freezes degrees freedom inside certain "arctic" region, determine numerically. evidence for existence logarithmic terms, generated by massless living outside arctic region.
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sci-hub.se 参考文章(123)
Tetsuji Miwa, Michio Jimbo, Algebraic Analysis of Solvable Lattice Models. ,(1994)
Barry Simon, Orthogonal polynomials on the unit circle ,(2004)
Michael E. Fisher, Robert E. Hartwig, Toeplitz Determinants: Some Applications, Theorems, and Conjectures John Wiley & Sons, Inc.. pp. 333- 353 ,(2007) , 10.1002/9780470143605.CH18
Peter Shor, James Propp, William Jockusch, Random Domino Tilings and the Arctic Circle Theorem arXiv: Combinatorics. ,(1998)
Michel Gaudin, La fonction d'onde de Bethe Masson. ,(1983)
Thierry Giamarchi, Quantum physics in one dimension ,(2004)
Pavel M. Bleher, Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions Springer, Dordrecht. pp. 59- 72 ,(2009) , 10.1007/978-90-481-2810-5_5
Masaki Oshikawa, Ian Affleck, Boundary conformal field theory approach to the critical two-dimensional Ising model with a defect line Nuclear Physics. ,vol. 495, pp. 533- 582 ,(1997) , 10.1016/S0550-3213(97)00219-8
H. Francis Song, Christian Flindt, Stephan Rachel, Israel Klich, Karyn Le Hur, Entanglement entropy from charge statistics: Exact relations for noninteracting many-body systems Physical Review B. ,vol. 83, pp. 161408- ,(2011) , 10.1103/PHYSREVB.83.161408
P.W. Kasteleyn, The statistics of dimers on a lattice Physica. ,vol. 27, pp. 1209- 1225 ,(1961) , 10.1016/0031-8914(61)90063-5