Signatures of coherent electronic quasiparticles in the paramagnetic Mott insulator

Abstract

We study the Mott insulating state of the half-filled paramagnetic Hubbard model within dynamical mean field theory using a recently formulated stochastic and nonperturbative quantum impurity solver. The method is based on calculating the impurity self energy as a sample average over a representative distribution of impurity models solved by exact diagonalization. Due to the natural parallelization of the method, millions of poles are readily generated for the self energy which allows us to work with very small pole-broadening $\ensuremath{\eta}$. Solutions at small and large $\ensuremath{\eta}$ are qualitatively different; solutions at large $\ensuremath{\eta}$ show featureless Hubbard bands whereas solutions at small $\ensuremath{\eta}\ensuremath{\le}0.001$ (in units of half bare band width) show a band of electronic quasiparticles with very small quasiparticle weight at the inner edge of the Hubbard bands. The validity of the results are supported by agreement within statistical error ${\ensuremath{\sigma}}_{\text{QMC}}\ensuremath{\sim}{10}^{\ensuremath{-}4}$ on the imaginary frequency axis with calculations using a continuous time quantum Monte Carlo solver. Nevertheless, convergence with respect to finite size of the stochastic exact diagonalization solver remains to be rigourously established.