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Raimundo R. dos Santos (UFRJ): Ferromagnetism beyond Lieb's theorem
19.04.2018 11.00 h
Sala 429 (torre nova) - Niterói


Seminário de Física da Matéria Condensada


19/04 - 5a feira - 11h00
Sala 429 - 4o andar da torre nova

Palestrante:  Raimundo Rocha dos Santos (UFRJ)

Título: Ferromagnetism beyond Lieb's theorem 


Modelling itinerant ferromagnetism still poses major challenges to theoreticians. In 1963 John Hubbard proposed [1] a single-band model, but, as it turned out, ferromagnetism only appears within mean-field approximations. Since then, distinct routes to ferromagnetism have been proposed, some of which are based on multi-band models. The development of this route was boosted by a theorem proved by Elliott Lieb [2], according to which the Hubbard model on bipartite lattices with unequal number of sites on each sublattice, and at half filling, should have a non-zero spin in the ground state. While a total non-zero spin is suggestive of long-range order (LRO), a systematic investigation of LRO had not been carried out so far. Another issue of interest is whether Lieb’s theorem can be extended to lattices in which the on-site repulsion is inhomogeneous. An example of a lattice falling under the conditions of the theorem is the ‘CuO2 lattice (also known as ‘Lieb lattice’, or as a decorated square lattice), in which ‘d-orbitals’ occupy the vertices of the squares, while ‘p-orbitals’ lie halfway between two d-orbitals; both d and p orbitals can accommodate only up to two electrons. In this talk we report on Determinant Quantum Monte Carlo (DQMC) simulations for the Lieb lattice [3]. We quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud = Up, originally considered by Lieb, and the inhomogeneous (IH) case, Ud ̸= Up. For the H case at half filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the 

antiferromagnetism between unlike sites; we verified that the system is an insulator for all U. For the IH system at half filling, we argue that the case Up ̸= Ud falls under Lieb’s theorem, provided they are positive definite, so we used DQMC to probe the cases Up =0,Ud =U andUp =U,Ud =0. We found that the different environments of d and p sites lead to a ferromagnetic insulator when Ud = 0; by contrast, Up = 0 leads to a metal without any magnetic ordering. In addition, we have also established that at density ρ = 1/3, strong antiferromagnetic correlations set in, caused by the presence of one fermion on each d site; this filling corresponds to a van Hove singularity in the density of states, and the Fermi surface is nested, similarly to what happens in the Hubbard model in the simple square lattice.

1. J Hubbard, Proc R Soc London Ser A 276, 238 (1963).
2. EH Lieb, Phys Rev Lett 62, 1201 (1989); (E) 62, 1927 (1989).
3. NC Costa, T Mendes-Santos, T Paiva, RR dos Santos, and RT Scalettar, Phys Rev B 94, 155107 (2016).



Sala 429 (torre nova)
Av. Gal. Milton Tavares de Sousa s/n
Country: br


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