Massive Corrections to Entanglement in Minimal E8 Toda Field Theory

In this letter we study the exponentially decaying corrections to saturation of the second Rényi entropy of one interval of length \ellℓ in minimal E_8E8 Toda field theory. It has been known for some time that the entanglement entropy of a massive quantum field theory in 1+1 dimensions saturates to a constant value for m_1\ell\gg 1m1ℓ≫1 where m_1m1 is the mass of the lightest particle in the spectrum. Subsequently, results by Cardy, Castro-Alvaredo and Doyon have shown that there are exponentially decaying corrections to this behaviour which are characterized by Bessel functions with arguments proportional to m_1\ellm1ℓ. For the von Neumann entropy the leading correction to saturation takes the precise universal form -\frac{1}{8}K_0(2m_1\ell)−18K0(2m1ℓ) whereas for the Rényi entropies leading corrections which are proportional to K_0(m_1\ell)K0(m1ℓ) are expected. Recent numerical work by Pálmai for the second Rényi entropy of minimal E_8E8 Toda has identified next-to-leading order corrections which decay as e^{-2m_1\ell}e−2m1ℓ rather than the expected e^{-m_1\ell}e−m1ℓ. In this paper we investigate the origin of this result and show that it is incorrect. An exact form factor computation of correlators of branch point twist fields reveals that the leading corrections are proportional to K_0(m_1 \ell)K0(m1ℓ) as expected.