Ferromagnetism beyond Lieb's theorem

Journal Article · Thu Oct 06 00:00:00 EDT 2016 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.94.155107· OSTI ID:1477007

Costa, Natanael C. ^[1]; Mendes-Santos, Tiago ^[2]; Paiva, Thereza ^[2]; Santos, Raimundo R. dos ^[2]; Scalettar, Richard T. ^[3]

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1. Univ. Federal do Rio de Janeiro, Rio de Janeiro (Brazil). Inst. de Fisica; The Regents of the University of California, Davis
2. Univ. Federal do Rio de Janeiro, Rio de Janeiro (Brazil). Inst. de Fisica
3. Univ. of California, Davis, CA (United States). Dept. of Physics

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. Here, we study both the homogeneous (H) case, U_d = U_p, originally considered by Lieb, and the inhomogeneous (IH) case, U_d ≠ U_p. 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 U_p ≠ U_d falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases U_p = 0, U_d = U and Up = U, U_d = 0. We found that the different environments of d and p sites lead to a ferromagnetic insulator when U_d = 0; by contrast, U_p = 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.

• Research Organization: Univ. of California, Davis, CA (United States)
• Sponsoring Organization: USDOE; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: NA0002908; SC0014671
• OSTI ID: 1477007
• Alternate ID(s): OSTI ID: 1328225
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 15 Vol. 94; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY