  We consider the reflected entropy and the associated entanglement spectrum
for free fermions reduced to two intervals in 1+1 dimensions. Working directly
in the continuum theory the reflected entropy can be extracted from the
spectrum of a singular integral equation whose kernel is determined by the
known free fermion modular evolved correlation function. We find the spectrum
numerically and analytically in certain limits. For intervals that almost touch
the reflected entanglement spectrum approaches the spectrum of the thermal
density matrix. This suggests that the reflected entanglement spectrum is well
suited to the task of extracting physical data of the theory directly from the
ground state wave function.
