Finite-size corrections of the Entanglement Entropy of critical quantum chains

TL;DR

This paper investigates finite-size corrections to the entanglement entropy in various critical quantum chains using DMRG, revealing their connection to conformal field theory operators and proposing general conjectures for the correction exponents.

Contribution

It provides a comprehensive analysis of finite-size corrections across different models and formulates conjectures linking these corrections to operator dimensions in conformal field theory.

Findings

Finite-size correction amplitudes depend on the Renyi index and relate to operator dimensions.

Conjecture that the correction exponent p_α equals 2X_ε/α for α>1.

Leading correction exponent p_1 equals 2 for all models.

Abstract

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.