Spatially resolved dynamic susceptibilities of disordered two dimensional Hubbard model

We predict the existence of an emergent metallic phase in the disordered two dimensional Hubbard model [1] that has recently been confirmed by experiments on 1T-TaS$_2$ intercalated with Cu. The metallic state has a finite dc conductivity but unusual dynamical properties. We present here a comprehensive analysis of the spatially resolved spin susceptibility, screened charge density, and optical conductivity of the disordered Hubbard model. We develop a new method in which the exact eigenstates from inhomogeneous mean-field theory are used to calculate dynamical susceptibilities within the random phase approximation. By combining the non-perturbative effects of self-consistent mean-field theory with analytical perturbative methods, this approach gives insights about fluctuations near the quantum phase transitions. We make several predictions which can be directly tested in spatially resolved experiments. \\[4pt] [1] D. Heidarian and N. Trivedi, Phys. Rev. Lett. {\bf 93}, 126401 (2004)