We consider diagonal matrix elements of local operators between multi-soliton states in finite volume in the sine-Gordon model, and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Takács which were only valid for diagonal scattering. In order to test the conjecture we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.

Abstract. We discuss the Rényi entanglement entropies of descendant states in critical onedimensional systems with boundaries, that map to boundary conformal field theories in the scaling limit. We unify the previous conformal-field-theory approaches to describe primary and descendant states in systems with both open and closed boundaries. We provide universal expressions for the first two descendants in the identity family. We apply our technique to critical systems belonging to different universality classes with non-trivial boundary conditions that preserve conformal invariance, and find excellent agreement with numerical results obtained for finite spin chains. We also demonstrate that entanglement entropies are a powerful tool to resolve degeneracy of higher excited states in critical lattice models.

We study entanglement via the subsystem purity relative to bipartitions of arbitrary excited states in (1+1)dimensional conformal field theory, equivalent to the scaling limit of one dimensional quantum critical systems. We compute the exact subpurity as a function of the relative subsystem size for numerous excited states in the Ising and three-state Potts models. We find that it decays exponentially when the system and the subsystem sizes are comparable until a saturation limit is reached near half-partitioning, signaling that excited states are maximally entangled. The exponential behavior translates into extensivity for the second Rényi entropy. Since the coefficient of this linear law depends only on the excitation energy, this result shows an interesting, new relationship between energy and quantum information and elucidates the role of microscopic details.