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Emptiness Formation Probability in the XY Model

Fabio Franchini, Alexander G. Abanov

APSMar 1, 20040 citations

Emptiness formation probability and quantum Knizhnik–Zamolodchikov equation

Herman E. Boos, V. E. Korepin, Fedor Aleksandrovich Smirnov

arXiv:hep-th/0209246Nuclear Physics BApr 25, 200374 citations

Emptiness formation probability in the domain-wall six-vertex model

Filippo Colomo, A. G. Pronko

arXiv:0712.1524Nuclear Physics BDec 28, 200751 citations

Emptiness formation probability of XX-chain in diffusion process

Yoshiko Ogata

Chaos Solitons & FractalsAug 7, 20030 citations

A new correlator in quantum spin chains

Jonathan P. Keating, Francesco Mezzadri, Marcel Novaes

We propose a new correlator in one-dimensional quantum spin chains, the s -emptiness formation probability ( s -EFP). This is a generalization of the emptiness formation probability (EFP), which is the probability that the first n spins of the chain are all aligned downwards. In the s -EFP we let the spins in question be separated by s sites. The usual EFP corresponds to the special case when s = 1. Taking s > 1 allows us to quantify non-local correlations. We express the s -EFP for the anisotropic XY model in a transverse magnetic field, a system with both critical and non-critical regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find that the magnetic field induces an interesting length scale.We propose a new correlator in one-dimensional quantum spin chains, the s -emptiness formation probability ( s -EFP). This is a generalization of the emptiness formation probability (EFP), which is the probability that the first n spins of the chain are all aligned downwards. In the s -EFP we let the spins in question be separated by s sites. The usual EFP corresponds to the special case when s = 1. Taking s > 1 allows us to quantify non-local correlations. We express the s -EFP for the anisotropic XY model in a transverse magnetic field, a system with both critical and non-critical regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find that the magnetic field induces an interesting length scale.

arXiv:cond-mat/0604173Journal of Physics A Mathematical and GeneralMay 31, 20064 citations

EMPTINESS FORMATION PROBABILITY AND QUANTUM KNIZHNIK-ZAMOLODCHIKOV EQUATION

Herman E. Boos, V. E. Korepin, Fedor Aleksandrovich Smirnov

We consider the one-dimensional XXX spin 1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of a formation of a ferromagnetic string P(n) in the antiferromagnetic ground-state. We call it emptiness formation probability [EFP]. We suggest a new technique for computation of the EFP in the inhomogeneous case. It is based on the quantum Knizhnik-Zamolodchikov equation [qKZ]. We calculate EFP for n≤6 for the inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations and number theory. We also make a conjecture about a structure of EFP for arbrary n.We consider the one-dimensional XXX spin 1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of a formation of a ferromagnetic string P(n) in the antiferromagnetic ground-state. We call it emptiness formation probability [EFP]. We suggest a new technique for computation of the EFP in the inhomogeneous case. It is based on the quantum Knizhnik-Zamolodchikov equation [qKZ]. We calculate EFP for n≤6 for the inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations and number theory. We also make a conjecture about a structure of EFP for arbrary n.

International Journal of Modern Physics AMay 1, 20045 citations

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