Prethermalization in the transverse-field Ising chain with long-range interactions

Nonequilibrium dynamics of an isolated quantum spin chain with long-range Ising interactions that decay as $1/r^\alpha$ ($0<\alpha<1$) with the distance $r$ is studied. It turns out that long-range interactions give rise to a big timescale separation, which causes prethermalization for all $\alpha\in(0,1)$. This conclusion is deduced by comparing two important timescales relevant for relaxation dynamics; one is the relaxation time of local permutation operators, which are quasi-conserved quantities in this system, and the other is the timescale of the initial relaxation due to the growth of quantum fluctuations. We also explore the entire nonequilibrium dynamics by using the discrete truncated Wigner approximation, which is consistent with the result mentioned above.