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We analyze many-body localization (MBL) to delocalization transition inSherrington-Kirkpatrick (SK) model of Ising spin glass (SG) in the presence ofa transverse field $\Gamma$. Based on energy resolved analysis, which is ofrelevance for a closed quantum system, we show that the quantum SK model hasmany-body mobility edges separating MBL phase which is non-ergodic andnon-thermal from the delocalized phase which is ergodic and thermal. The rangeof the delocalized regime increases with increase in the strength of $\Gamma$and eventually for $\Gamma$ larger than $\Gamma_{CP}$ the entire many-bodyspectrum is delocalized. We show that the Renyi entropy is almost independentof the system size in the MBL phase, hinting towards an area law in thisinfinite range model while the delocalized phase shows volume law scaling ofRenyi entropy. We further obtain spin glass transition curve in energy density$\epsilon$-$\Gamma$ plane from the collapse of eigenstate spin susceptibility.We demonstrate that in most of the parameter regime SG transition occurs closeto the MBL transition indicating that the SG phase is non-ergodic andnon-thermal while the paramagnetic phase is delocalized and thermal.

Many body localization-delocalization transition in quantum Sherrington-Kirkpatrick model