Entanglement Entropies in Conformal Systems with Boundaries

TL;DR

This paper investigates how entanglement entropies behave in one-dimensional critical systems with boundaries, revealing finite-size effects linked to the underlying conformal field theory and confirming results through numerical analysis.

Contribution

It provides analytical expressions for entanglement entropies in boundary conformal systems and validates them with numerical simulations for specific models.

Findings

Entanglement entropies depend on boundary conditions and system size.

Analytical results agree with numerical simulations for models with c=1/2 and c=1.

Finite-size effects are characterized by the underlying conformal field theory.

Abstract

We study the entanglement entropies in one-dimensional open critical systems, whose effective description is given by a conformal field theory with boundaries. We show that for pure-state systems formed by the ground state or by the excited states associated to primary fields, the entanglement entropies have a finite-size behavior that depends on the correlation of the underlying field theory. The analytical results are checked numerically, finding excellent agreement for the quantum chains ruled by the theories with central charge $c=1/2$ and $c=1$.