Universal Thermal Corrections to Single Interval Entanglement Entropy for Two Dimensional Conformal Field Theories

We consider single interval Rényi and entanglement entropies for a two dimensional conformal field theory on a circle at nonzero temperature. Assuming that the finite size of the system introduces a unique ground state with a nonzero mass gap, we calculate the leading corrections to the Rényi and entanglement entropy in a low temperature expansion. These corrections have a universal form for any two dimensional conformal field theory that depends only on the size of the mass gap and its degeneracy. We analyze the limits where the size of the interval becomes small and where it becomes close to the size of the spatial circle.

Figure 1

Thermal corrections to entanglement entropy $\delta S_E=S_E(T)-S_E(0)$ plotted against $\ell /L$ for a free, massless ($1+1$) dimensional fermion. The points are numerically determined from a lattice model of size $N=100$ grid points using the method described in Refs. [9, 15]. $L$ is the size of the circle and $\ell$ the size of the interval. From top to bottom, the points correspond to $LT=0.15$, 0.2, 0.3, 0.4, 0.5. The solid curve is the prediction (6). Inset: $\delta S_E$ plotted against $LT$ for $\ell =L$. The curve is the thermal entropy correction $4(1+\pi /LT)$.