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International Journal of Theoretical and Mathematical Physics

Theorems to Demonstrate the Presence of Antiferromagnetism in the Periodic Anderson Model

Omamoke O. E. Enaroseha, Ejiroghene G. Akpojotor, Lawrence Atuma

Published Jan 1, 2014• 2 citations
OpenAlex

Abstract

Anderson model is an important model in the theory of strongly correlated electron system. In this study, we explore the ground state of this model and the concept of electron correlation by bipartite lattice and prove rigorously theorems leading to the presence of spin singlet in the model. By using the results of Ueda et al [15] and Tian [16], we show theoretically that the ground state of the symmetric periodic Anderson model has a short – range order antiferromagnetism.

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THEOREMS TO DEMOSTRATE THE PRESENCE OF ANTIFERROMAGNETISM IN THE PERIODIC ANDERSON MODEL.

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Anderson model is an important model in the theory of strongly correlated electron system.In this contribution, we introduce this model and the concept of electron correlation by bipartite lattice and prove rigorously theorems leading to the presence of spin singlet in the model.By using the results of Ueda et al (1992) and Tian (1994), we show theoretically that the ground state of the symmetric periodic Anderson model has a short -range order.1.0.

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Rigorous results for the one-dimensional symmetric Anderson model

Canio Noce, Mario Cuoco

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Physical review. B, Condensed matter•Nov 1, 1996•5 citations
Anderson model is an important model in the theory of strongly correlated electron system. In this study, we explore the ground state of this model and the concept of electron correlation by bipartite lattice and prove rigorously theorems leading to the presence of spin singlet in the model. By using the results of Ueda et al [15] and Tian [16], we show theoretically that the ground state of the symmetric periodic Anderson model has a short – range order antiferromagnetism.
Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matrix embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin–spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin–spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.
As an extension of our previous rigorous investigation on the spin correlations in the ground states of the half-filled Hubbard model and the periodic Anderson model [G. S. Tian, Phys. Rev. B 50, 6246 (1994)], in the present paper we study the behavior of these correlation functions at finite temperature. We show rigorously that, at any $T\ensuremath{\ne}0,$ the predominant spin correlations in these systems are antiferromagnetic. Furthermore, based on this result, we also show that a quasi-one (or two)-dimensional itinerant electron ferrimagnet must have a gapless branch of ferromagnetic excitations. This conclusion is consistent with the previous results derived by the spin-wave theory.