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Spatial Correlations and the Insulating Phase of the High-$T_c$ Cuprates: Insights from a Configuration-Interaction-Based Solver for Dynamical Mean Field Theory

A recently proposed configuration-interaction based impurity solver is used in combination with the single-site and four-site cluster dynamical mean field approximations to investigate the three-band copper oxide model believed to describe the electronic structure of high transition temperature copper-oxide superconductors. Use of the configuration interaction solver enables verification of the convergence of results with respect to the number of bath orbitals. The spatial correlations included in the cluster approximation substantially shift the metal-insulator phase boundary relative to the prediction of the single-site approximation and increase the predicted energy gap of the insulating phase by about 1 eV above the single-site result. Vertex corrections occurring in the four-site approximation act to dramatically increase the value of the optical conductivity near the gap edge, resulting in a better agreement with the data. The calculations reveal two distinct correlated insulating states: the `magnetically correlated insulator', in which nontrivial intersite correlations play an essential role in stabilizing the insulating state, and the strongly correlated insulator, in which local physics suffices. Comparison of the calculations to the data place the cuprates in the magnetically correlated Mott insulator regime.