+We study the one-particle entanglement entropy of spinless interacting fermions in the Tomonaga-Luttinger liquid regime, both at equilibrium and after an interaction quantum quench. Using both large scale exact diagonalization and time-dependent density matrix renormalization group calculations, we numerically compute the one-body reduced density matrix for the J-V model and its time evolution at large system sizes. We study both the growth of the entanglement entropy after the quench and the interaction dependence of its steady state value, and use finite size scaling of the numerical data for large system sizes to extrapolate to the thermodynamic limit. To compare these numerical results with analytic results obtained through bosonization of the fermionic fields, we determine the value of an interaction cutoff such that numerical results for the entanglement entropy in equilibrium are reproduced. We then find excellent agreement between numerical and field theoretical results as long as the quench does not approach the quantum liquid phase boundaries.
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