Slave Particle Studies of the Electron Momentum Distribution in the Low Dimensional $t-J$ Model

The electron momentum distribution function in the $t-J$ model is studied in the framework of slave particle approach. Within the decoupling scheme used in the gauge field and related theories, we treat formally phase and amplitude fluctuations as well as constraints without further approximations. Our result indicates that the electron Fermi surface observed in the high-resolution angle-resolved photoemission and inverse photoemission experiments cannot be explained within this framework, and the sum rule for the physical electron is not obeyed. A correct scaling behavior of the electron momentum distribution function near $k \sim k_{F}$ and $k \sim 3k_{F}$ in one dimension can be reproduced by considering the nonlocal string fields [Z. Y. Weng et al., Phys. Rev. B45, 7850 (1992)], but the overall momentum distribution is still not correct, at least at the mean field level.