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We consider the target space entanglement in quantum mechanics ofnon-interacting fermions at finite temperature. Unlike pure states investigatedin arXiv:2105.13726, the (R\'enyi) entanglement entropy for thermal states doesnot follow a simple bound because all states in the infinite-dimensionalHilbert space are involved. We investigate a general formula of the targetspace R\'enyi entropy for $N$ fermions at finite temperature, and presentnumerical results of the entropy in a one-dimensional model. We also argue thelarge $N$ behaviors with a comparison to the grand canonical ensemble.

Target space entanglement in quantum mechanics of fermions at finite temperature