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Physical Review Letters

Exact diagonalization approach to correlated fermions in infinite dimensions: Mott transition and superconductivity

Michel Caffarel, Werner Krauth

Published Mar 7, 1994• 634 citations
Publisher

Abstract

We present a powerful method for calculating the thermodynamic properties of infinite-dimensional Hubbard-type models using an exact diagonalization of an Anderson model with a finite number of sites. The resolution obtained for Green's functions is far superior to that of quantum Monte Carlo calculations. We apply the method to the half-filled Hubbard model for a discussion of the metal-insulator transition, and to the two-band Hubbard model where we find direct evidence for the existence of a superconducting instability at low temperatures.

DOI
10.1103/physrevlett.72.1545

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We present a powerful method for calculating the thermodynamic properties of infinite-dimensional Hubbard-type models using an exact diagonalization of an Anderson model with a finite number of sites. The resolution obtained for Green's functions is far superior to that of quantum Monte Carlo calculations. We apply the method to the half-filled Hubbard model for a discussion of the metal-insulator transition, and to the two-band Hubbard model where we find direct evidence for the existence of a superconducting instability at low temperatures.
We present a powerful method for calculating the thermodynamic properties of the Hubbard model in infinite dimensions, using an exact diagonalization of an Anderson model with a finite number of sites. At finite temperatures, the explicit diagonalization of the Anderson Hamiltonian allows the calculation of Green's functions with a resolution far superior to that of Quantum Monte Carlo calculations. At zero temperature, the Lanczòs method is used and yields the essentially exact zero-temperature solution of the model, except in a region of very small frequencies. Numerical results for the half-filled case in the paramagnetic phase (quasi-particle weight, self-energy, and also real-frequency spectral densities) are presented.
We apply an exact diagonalization method to the the infinite-D two-band Hubbard model. The method is essentially exact for the calculation of thermodynamic properties for all but the smallest frequencies and yields a resolution unavailable in Monte Carlo calculations. We establish the instability of the normal state with respect to singlet superconductivity at small frequencies at small doping, the regime of relevance for High-TcT_cTc​ superconductors. We also present evidence for the existence of an instability towards triplet superconductivity in the large doping regime n∼2n \sim 2n∼2.
We present a numerical solution of the infinite-dimensional Hubbard model at finite temperature in the paramagnetic phase. The problem reduces to a single-impurity Anderson model supplemented by a self-consistency condition. Using Monte Carlo methods and complete enumeration we determine the imaginary-time Green's function, the density of doubly occupied sites, and the compressibility close to half filling. All three quantities present direct evidence for a Mott insulating phase above a critical value of U.
We use determinant quantum Monte Carlo simulations and exact diagonalization to explore insulating behavior in the Hubbard model with a bimodal distribution of randomly positioned local site energies. From the temperature dependence of the compressibility and conductivity, we show that gapped, incompressible Mott insulating phases exist away from half-filling when the variance of the local site energies is sufficiently large. The compressible regions around this Mott phase are metallic only if the density of sites with the corresponding energy exceeds the percolation threshold, but are Anderson insulators otherwise.