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arXiv:cond-mat/9908221 · Physical review. B, Condensed matter

Coexistence of solutions in dynamical mean-field theory of the Mott transition

Werner Krauth

Published Sep 15, 2000• 14 citations
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Abstract

In this paper, I discuss the finite-temperature metal-insulator transition of the paramagnetic Hubbard model within dynamical mean-field theory. I show that coexisting solutions, the hallmark of such a transition, can be obtained in a consistent way both from quantum Monte Carlo (QMC) simulations and from the exact diagonalization method. I pay special attention to discretization errors within the QMC method. These errors explain why it is difficult to obtain the solutions from the QMC method close to the boundaries of the coexistence region.

DOI
10.1103/physrevb.62.6860

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In this paper, I discuss the finite-temperature metal-insulator transition of the paramagnetic Hubbard model within dynamical mean-field theory. I show that coexisting solutions, the hallmark of such a transition, can be obtained in a consistent way both from quantum Monte Carlo (QMC) simulations and from the exact diagonalization method. I pay special attention to discretization errors within the QMC method. These errors explain why it is difficult to obtain the solutions from the QMC method close to the boundaries of the coexistence region.
We present clear numerical evidence for the coexistence of metallic and insulating dynamical mean-field theory (DMFT) solutions in a half-filled single-band Hubbard model at finite temperature. The quantum Monte Carlo (QMC) method is used to solve the DMFT equation. We discuss important technical aspects of the DMFT-QMC method, which should be properly dealt with in order to obtain reliable DMFT solutions at low temperatures. Among these technical aspects are the critical slowing down near the boundaries of the coexistence region, the convergence criteria for the DMFT iterations, and the correct interpolation of the discretized Green's functions.
We consider a Mott transition of the Hubbard model in infinite dimensions. The dynamical meanfield theory is employed in combination with a continuous-time quantum Monte Carlo (CTQMC) method for an accurate description at low temperatures. From the double occupancy and the energy density, which are directly measured from the CTQMC method, we construct the phase diagram. We pay particular attention to the construction of the first-order phase transition line (PTL) in the coexistence region of metallic and insulating phases. The resulting PTL is found to exhibit reasonable agreement with earlier finite-temperature results. We also show by a systematic inclusion of low-temperature data that the PTL, which is achieved independently of the previous zero-temperature results, approaches monotonically the transition point from earlier zerotemperature studies.
We investigate paramagnetic metal-insulator transitions in the infinite-dimensional ionic Hubbard model at finite temperatures. By means of the dynamical mean-field theory with an impurity solver of the continuous-time quantum Monte Carlo method, we show that an increase in the interaction strength brings about a crossover from a band insulating phase to a metallic one, followed by a first-order transition to a Mott insulating phase. The first-order transition turns into a crossover above a certain critical temperature, which becomes higher as the staggered lattice potential is increased. Further, analysis of the temperature dependence of the energy density discloses that the intermediate metallic phase is a Fermi liquid. It is also found that the metallic phase is stable against strong staggered potentials even at very low temperatures.
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.
From the Hubbard model,we calculated the Green's function of the system with the dynamical mean-field theory and the quantum Monte Carlo simulation.We also had a thorough discussion on the numerical results of the Green's function in paramagnetic and antiferromagnetic orders and gave the variations of Green's function at different temperatures and different Hubbard energies.From the analysis of these results,we concluded that with the decrease of the temperature or the increase of the Hubbard energy,the system would have Mott transition from metal to insulator.