A single-eigenstate ETH diagnostic based on the time-averaged evolution speed after a perturbed eigenstate quench is proposed, with an S-curve versus J-curve shape distinction benchmarked on small spin chains.
S+ j =S x j + iSy j being the standard local spin-1raising operator
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Single-eigenstate test of eigenstate thermalization hypothesis via perturbed eigenstate quench
A single-eigenstate ETH diagnostic based on the time-averaged evolution speed after a perturbed eigenstate quench is proposed, with an S-curve versus J-curve shape distinction benchmarked on small spin chains.