Numerical Solution of the $t\mathrm{\text{−}}J$ Model with Random Exchange Couplings in $d\mathbf{=}\infty$ Dimensions

To explore the nature of the metallic state near the transition to a Mott insulator, we investigate the $t\mathrm{\text{−}}J$ model with random exchange interaction in $d=\infty$ dimensions. A numerically exact solution is obtained by an extension of the continuous-time quantum Monte Carlo method to the case of a vector bosonic field coupled to a local spin. We show that the paramagnetic solution near the Mott insulator describes an incoherent metal with a residual moment, and that single-particle excitations produce an additional band, which is separated from the Mott-Hubbard band.