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arXiv:cond-mat/9306057

Exact Diagonalization Approach for the infinite D Hubbard Model

Michel Caffarel, Werner Krauth

Published Jun 28, 1993• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/9306057

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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.
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We develop a method for calculating the self-energy of a quantum impurity coupled to a continuous bath by stochastically generating a distribution of finite Anderson models that are solved by exact diagonalization, using the noninteracting local spectral function as a probability distribution for the sampling. The method enables calculation of the full analytic self-energy and single-particle Green's function in the complex frequency plane, without analytic continuation, and can be used for both finite and zero temperature at arbitrary fillings. Results are in good agreement with imaginary frequency data from continuous-time quantum Monte Carlo calculations for the single-impurity Anderson model and the two-orbital Hubbard model within dynamical mean-field theory (DMFT) as well as real frequency data for self-energy of the single-band Hubbard model within DMFT using the numerical renormalization group. The method should be applicable to a wide range of quantum impurity models and particularly useful when high-precision real frequency results are sought.
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 detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Hubbard model with diagonal disorder (Anderson-Hubbard model) is investigated analytically and numerically in the limit of infinite spatial dimensions, i.e., within a dynamical mean-field theory, at half-filling. Numerical results are obtained for three different disorder distributions by employing quantum Monte Carlo techniques, which provide an explicit finite-temperature solution of the model in this limit. The magnetic phase diagram is constructed from the zeros of the inverse averaged staggered susceptibility. We find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A strong coupling anomaly, i.e., an increase of the N\'eel temperature for increasing disorder, is discovered. An explicit explanation is given, which shows that in the case of diagonal disorder this is a generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phases. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.