Odd entanglement entropy and logarithmic negativity for thermofield double states

A bstract We investigate the time evolution of odd entanglement entropy (OEE) and logarithmic negativity (LN) for thermofield double (TFD) states in free scalar quantum field theories using covariance matrix approach. To have mixed states, we choose non-complementary subsystems, either adjacent or disjoint intervals on each side TFD. find that pattern OEE is a linear growth followed by saturation. On circular lattice, longer times finite size effect demonstrates itself as oscillatory behavior. In limit vanishing mass, subsystem containing single degree freedom TFD, analytically zero-mode which leads to intermediate times. Moreover, LN zero t < ?/ 2 (half inverse temperature) after that, it begins grow linearly. For at fixed temperature, observed d/ distance between intervals). also similar delay see ? S = ? EE . All these results show dynamics measures are consistent with quasi-particle picture, course apart from growth.