Negative electron compressibility in the Hubbard Model

Using the strong coupling diagram technique, we study the one-band repulsive Hubbard model on a two-dimensional square lattice in a wide range of chemical potentials $\mu$. Infinite sequences of diagrams describing interactions of electrons with spin and charge fluctuations are taken into account. At low temperatures, regions of the negative electron compressibility are found for $\mu <0$ and $\mu >U$, where $U$ is the Hubbard repulsion. For even lower temperatures, in the neighborhood of these regions, states with the phase separation are revealed.