1111.6577 (J. C. Xavier et al.)

Finite-size corrections of the Entanglement Entropy of critical quantum
chains    [PDF]

J. C. Xavier, F. C. Alcaraz

Using the density matrix renormalization group, we calculated the finite-size
corrections of the entanglement $\alpha$-Renyi entropy of a single interval for
several critical quantum chains. We considered models with U(1) symmetry like
the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well models with
discrete symmetries such as the Ising, the Blume-Capel and the three-state
Potts models. These corrections contain physically relevant information. Their
amplitudes, that depend on the value of $\alpha$, are related to the dimensions
of operators in the conformal field theory governing the long-distance
correlations of the critical quantum chains. The obtained results together with
earlier exact and numerical ones allow us to formulate some general conjectures
about the operator responsible for the leading finite-size correction of the
$\alpha$-Renyi entropies. We conjecture that the exponent of the leading
finite-size correction of the $\alpha$-Renyi entropies is
$p_{\alpha}=2X_{\epsilon}/\alpha$ for $\alpha>1$ and $p_{1}=\nu$, where
$X_{\epsilon}$ is the dimensions of the energy operator of the model and
$\nu=2$ for all the models.

View original: http://arxiv.org/abs/1111.6577