  We study the entanglement dynamics of thermofield double (TFD) states in
integrable spin chains and quantum field theories. We show that, for a natural
choice of the Hamiltonian eigenbasis, the TFD evolution may be interpreted as a
quantum quench from an initial state which is low-entangled in the real-space
representation and displays a simple quasiparticle structure. Based on a
semiclassical picture analogous to the one developed for standard quantum
quenches, we conjecture a formula for the entanglement dynamics, which is valid
for both discrete and continuous integrable field theories, and expected to be
exact in the scaling limit of large space and time scales. We test our
conjecture in two prototypical examples of integrable spin chains, where
numerical tests are possible. First, in the XY-model, we compare our
predictions with exact results obtained by mapping the system to free fermions,
finding excellent agreement. Second, we test our conjecture in the interacting
XXZ Heisenberg model, against numerical iTEBD calculations. For the latter, we
generally find good agreement, although, for some range of the system
parameters and within the accessible simulation times, some small discrepancies
are visible, which we attribute to finite-time effects.
