Electronic Compressibility and Magnetic Susceptibility in the Repulsive Hubbard Model away from Half-Filling*

The Hubbard Model, noteworthy for its simplicity, is observed to possess multiple fascinating quantum phase transitions with rich physics and implications that have yet to be explored thoroughly. We quantitatively examine the response functions, electronic compressibility (κ) and magnetic susceptibility (χ), in the Repulsive Fermi-Hubbard model using Quantum Monte Carlo (QMC) techniques within the parameter space of temperature and interactions away from half filling. The equivalence of these response functions in the t >>U metallic phase is noted; and an analytic relation between κ and χ is derived as a function of density correlators. We analyze the phase diagram of the Fermi-Hubbard Model and suggest a likely, novel non-Fermi Liquid phase, as well as discuss the significance and consequences of such a phase.