Ferromagnetism beyond Lieb's theorem

Natanael C. Costa, Tiago Mendes-Santos, Thereza Paiva, Raimundo R. dos Santos, and Richard T. Scalettar
Phys. Rev. B 94, 155107 – Published 6 October 2016

Abstract

The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction U is turned on, Lieb proved rigorously that at half-filling (ρ=1) the ground state has a nonzero spin. In this paper we consider a “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. We use exact determinant quantum Monte Carlo (DQMC) simulations to 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, UdUp. 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 UpUd falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases Up=0,Ud=U and Up=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 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.

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  • Received 13 June 2016
  • Revised 13 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.155107

©2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Natanael C. Costa1, Tiago Mendes-Santos1, Thereza Paiva1, Raimundo R. dos Santos1, and Richard T. Scalettar2

  • 1Instituto de Fisica, Universidade Federal do Rio de Janeiro Cx.P. 68.528, 21941-972 Rio de Janeiro RJ, Brazil
  • 2Department of Physics, University of California, Davis, California 95616, USA

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Issue

Vol. 94, Iss. 15 — 15 October 2016

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