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We report in this paper our numerical analysis of energy level spacingstatistics for the one-dimensional spin-$1/2$ XXZ model in random on-sitelongitudinal magnetic fields $B_i$ ($-h\leq B_i\leq h$)). We concentrate on thestrong disorder limit $J_{\perp}<<J_z,h)$ where $J_z$ and $J_{\perp}$ are the(nearest neighbor) spin interaction strength in $z$- and planar ($xy$)-directions, respectively. The system is expected to be in a many-body localized(MBL) state in this parameter regime. By analyzing the energy-level spacingstatistics as a function of strength of random magnetic field $h$, energy ofthe many-body state $E$, the number of spin-$\uparrow$ particles in the system$M=\sum_i(s_i^z+{1\over2})$ and the spin interaction strengths $J_z$ and$J_{\perp}$, we show that there exists a small parameter region $J_z\sim h$where ergodic behaviour emerges at the middle of the many-body energy spectrumwhen $M\sim{N\over2}$ ($N=$ length of spin chain). The emerging ergodic phaseshows qualitatively different behaviour compared with the usual ergodic phasethat exists in the weak-disorder limit.

Emerging ergodic behavior within many-body localized states