Time Direction Entanglement Entropy of Free Fermion Ground States

arXiv:2611.13085v1 Announce Type: new Abstract: While the entanglement entropy of a spatial subregion has been extensively studied, a properly defined entanglement entropy of quantum states in a time direction interval remains underexplored. We investigate the scaling behaviors of the recently defined time direction entanglement entropy (TDEE) for free fermion quantum states, which is computed from the reduced density matrix of a sub-Hilbert space that minimally supports all the time-evolved operators in the time direction interval. Based on the Fisher--Hartwig conjecture for Toeplitz matrices, we develop an analytical framework for understanding the TDEE in a time interval with discrete time step $\tau$.