2005/02/11 by Fabio Franchini, Alexander G. Abanov, Alexander G Abanov
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bosonization #Chain (unit) #Classical XY model #Exponential function #Gaussian #Integrable system #Phase diagram #Quantum many-body systems #Spin (aerodynamics) #String (physics) #Theoretical and Computational Physics #Toeplitz matrix #cond-mat.str-el #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0305-4470/38/23/002
published as J.Phys. A38 (2005) 5069-5096 · 40 pages, 9 figures, 1 table. The poor quality of some figures is due to arxiv space limitations. If You would like to see the pdf with good quality figures, please contact Fabio Franchini at "[email protected]"
arxiv created 2005/02/11 · openalex publication_date 2005/05/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study an asymptotic behaviour of a special correlator known as the emptiness formation probability (EFP) for the one-dimensional anisotropic XY spin-1/2 chain in a transverse magnetic field. This correlator is essentially the probability of formation of a ferromagnetic string of length n in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models. For the XY spin chain, the correlator can be expressed as the determinant of a Toeplitz matrix and its asymptotical behaviours for n → ∞ throughout the phase diagram are obtained using known theorems and conjectures on Toeplitz determinants. We find that the decay is exponential everywhere in the phase diagram of the XY model except on the critical lines, i.e. where the spectrum is gapless. In these cases, a power-law prefactor with a universal exponent arises in addition to an exponential or Gaussian decay. The latter Gaussian behaviour holds on the critical line corresponding to the isotropic XY model, while at the critical value of the magnetic field the EFP decays exponentially. At small anisotropy one has a crossover from the Gaussian to the exponential behaviour. We study this crossover using the bosonization approach.