  We investigate the second R\'enyi entropy of two intervals in the massless
Thirring model describing a self-interacting Dirac fermion in two dimensions.
Boson-fermion duality relating this model to a free compact boson theory
enables us to simplify the calculation of the second R\'enyi entropy, reducing
it to the evaluation of the partition functions of the bosonic theory on a
torus. We derive exact results on the second R\'enyi entropy, and examine the
dependence on the sizes of the intervals and the coupling constant of the model
both analytically and numerically. We also explore the mutual R\'enyi
information, a measure quantifying the correlation between the two intervals,
and find that it generally increases as the coupling constant of the Thirring
model becomes larger.
