“School of Particles And Accelerator”
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Paper IPM / Particles And Accelerator / 16780  


Abstract:  
We investigate the time evolution of odd entanglement entropy (OEE) and logarithmic negativity (LN) for the thermofield double (TFD) states in free scalar quantum field theories using the covariance matrix approach. To have mixed states, we choose noncomplementary subsystems, either adjacent or disjoint intervals on each side of the TFD. We find that the time evolution pattern of OEE is a linear growth followed by saturation. On a circular lattice, for longer times the finite size effect demonstrates itself as oscillatory behavior. In the limit of vanishing mass, for a subsystem containing a single degree of freedom on each side of the TFD, we analytically find the effect of zeromode on the time evolution of OEE which leads to logarithmic growth in the intermediate times. Moreover, for adjacent intervals we find that the LN is zero for times t<Î²/2 (half of the inverse temperature) and after that, it begins to grow linearly. For disjoint intervals at fixed temperature, the vanishing of LN is observed for times t<d/2 (half of the distance between intervals). We also find a similar delay to see linear growth of ï¿½?S=SOEEï¿½??SEE. All these results show that the dynamics of these measures are consistent with the quasiparticle picture, of course apart from the logarithmic growth.
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