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Physical review. B, Condensed matter

Ground state of the periodic anderson model: comparison of exact diagonalization and monte carlo results

D. P. Chen, J. Callaway

Published Dec 1, 1988• 11 citations
Publisher

Abstract

The ground-state properties of the symmetric periodic Anderson model on a one-dimensional lattice are studied by exact diagonalization for a small (four-site) cluster. Comparison is made with results obtained for a larger (sixteen-site) ring obtained by Monte Carlo techniques. Excellent agreement is found for the range of parameters considered.

DOI
10.1103/physrevb.38.11869

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Physical review. B, Condensed matter•Apr 1, 1993•22 citations
The ground-state properties of the symmetric periodic Anderson model on a one-dimensional lattice are studied by exact diagonalization for a small (four-site) cluster. Comparison is made with results obtained for a larger (sixteen-site) ring obtained by Monte Carlo techniques. Excellent agreement is found for the range of parameters considered.
The ground-state properties of the periodic Anderson model on one-dimensional chains from three to six sites are studied by exact diagonalization. An appropriate average over boundary conditions is found to be necessary in order to eliminate finite-size oscillations. In the weak-coupling limit, the results for the short-range correlations suggest a smooth transition from a ferromagnetic state at low electron concentration to an antiferromagnetic state at half-filling, rather than a sudden jump at a critical concentration.
Ground-state properties of the asymmetric Hubbard model are studied on one-dimensional clusters (rings) with N=6, 8, and 10 sites. The ground-state energy, correlation functions, and phase diagrams are determined for various sets of model parameters. Computations are performed both by exact diagonalization (for N=6) and by an approximate method by which correlation effects can be examined on larger clusters than exact diagonalization allows. In the limiting cases (one limit corresponds to the spinless Falicov-Kimball model and the other to the Hubbard model) our results agree quite well with those obtained analytically for infinite systems.
We investigate the ground-state properties of the periodic Anderson model on the square lattice across various band fillings. Employing the infinite projected entangled-pair states (iPEPS) technique, we can determine the magnetic ground states accurately and compare them to mean-field predictions to highlight the effects of quantum fluctuations. At half-filling, we analyze the transition between the antiferromagnetic and paramagnetic (Kondo singlet) phases as a function of hybridization and fff-level energy, finding excellent agreement with existing quantum Monte Carlo studies in the case of hybridization. For n=1.5n = 1.5n=1.5 electrons per site, we identify a novel correlated antiferromagnetic diagonal stripe phase as the ground state, which competes with its ferromagnetic partner state.
The ground-state energy, hybridization energy, momentum distributions, local magnetic moments, and magnetic phase diagram of the symmetric periodic Anderson model are calculated using a correlated wave function in d=1,2, and 3 dimensions. The wave function is obtained by applying a Gutzwiller projector on a recently proposed single-particle product state with spin-density wave order. Evaluations are performed with an approximate scheme that becomes exact in high dimensions. Comparison with Monte Carlo data by Blankenbecler et al. for d=1 shows that the results are remarkably accurate for all values of the coupling. Hence the results for d=2,3 can be expected to be even more accurate and may serve as benchmarks for future numerical work in d>1.