Target space entanglement in quantum mechanics of fermions at finite temperature

Abstract

We consider the target space entanglement in quantum mechanics of non-interacting fermions at finite temperature. Unlike pure states investigated in arXiv:2105.13726, the (Rényi) entanglement entropy for thermal states does not follow a simple bound because all states in the infinite-dimensional Hilbert space are involved. We investigate a general formula of the target space Rényi entropy for $N$ fermions at finite temperature, and present numerical results of the entropy in a one-dimensional model. We also argue the large $N$ behaviors with a comparison to the grand canonical ensemble.

34+12 pages, 37 figures

References in corpus (9)

• Entwinement and the emergence of spacetime
• The entanglement entropy of one-dimensional gases
• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• Holographic Holes in Higher Dimensions
• Gravitation and vacuum entanglement entropy
• Gauge Invariant Target Space Entanglement in D-Brane Holography
• Entanglement in the Quantum Hall Matrix Model
• Target space entanglement in quantum mechanics of fermions and matrices
• Target space entanglement in a matrix model for the bubbling geometry