We demonstrate that the sign structure of the t-J model on a hypercubic lattice is entirely different from that of a Fermi gas, by inspecting the high temperature expansion of the partition function up to all orders, as well as the multi-hole propagator of the half-filled state and the perturbative expansion of the ground state energy. We show that while the fermion signs can be completely gauged away by a Marshall sign transformation at half-filling, the bulk of the signs can be also gauged away in a doped case, leaving behind a rarified "irreducible" sign structure that can be enumerated easily by counting exchanges of holes with themselves and spins on their real space paths. Such a sparse sign structure implies a mutual statistics for the quantum states of the doped Mott insulator.
@article{arxiv.0802.0273,
title = {On the sign structure of doped Mott insulators},
author = {K. Wu and Z. Y. Weng and J. Zaanen},
journal= {arXiv preprint arXiv:0802.0273},
year = {2009}
}