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The development of polynomial cost solvers for correlated quantum impuritymodels, with controllable errors, is a central challenge in quantum many-bodyphysics, where these models find applications ranging from nano-science to thedynamical mean-field theory (DMFT). Here we describe how configurationinteraction (CI) approximations to exact diagonalization (ED) may be used assolvers in DMFT. CI approximations retain the main advantages of ED, such asthe ability to treat general interactions and off-diagonal hybridizations andto obtain real spectral information, but are of polynomial cost. Furthermore,their errors can be controlled by monitoring the convergence of physicalquantities as a function of the CI hierarchy. Using benchmark DMFTapplications, such as single-site DMFT of the 1D Hubbard model and $2\times 2$cluster DMFT of the 2D Hubbard model, we show that CI approximations allow usto obtain near-exact ED results for a tiny fraction of the cost. This is trueover the entire range of interaction strengths including "difficult" regimes,such as in the pseudogap phase of the 2D Hubbard model. We use the ability ofCI approximations to treat large numbers of orbitals to demonstrate convergenceof the bath representation in the $2\times 2$ cluster DMFT using a 24 bathorbital representation. CI approximations thus form a promising route to extendED to problems that are currently difficult to study using other solvers suchas continuous-time quantum Monte Carlo, including impurity models with largenumbers of orbitals and general interactions.

Truncated Configuration Interaction expansions as solvers for correlated quantum impurity models and dynamical mean field theory