  In this work we report on a loss of ergodicity in a simple hopping model,
motivated by the Hubbard Hamiltonian, of a many body quantum system at zero
temperature, quantized in Euclidean time. We show that this quantum system may
lose ergodicity at high densities on a large lattice, as a result of both Pauli
exclusion and strong Coulomb repulsion. In particular we study particle hopping
susceptibilities and the tendency towards particle localization. It is found
that the appearance and existence of quantum phase transitions in this model,
in the case of high density and strong Coulomb repulsion, depends on the
starting configuration of particle trajectories in the numerical simulation. We
argue that this breakdown may be the Euclidean time version of a breakdown of
the eigenstate thermalization hypothesis in real time quantization.
