skip to main content

DOE PAGESDOE PAGES

Title: Ferromagnetism beyond Lieb's theorem

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 “CuO 2 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 magnetizationmore » 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.« less
Authors:
 [1] ;  [1] ;  [1] ;  [1] ;  [2]
  1. Univ. Federal do Rio de Janeiro, Rio de Janeiro (Brazil). Inst. de Fisica
  2. Univ. of California, Davis, CA (United States). Dept. of Physics
Publication Date:
Grant/Contract Number:
NA0002908; SC0014671
Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 94; Journal Issue: 15; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Research Org:
Univ. of California, Davis, CA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE
OSTI Identifier:
1477007
Alternate Identifier(s):
OSTI ID: 1328225

Costa, Natanael C., Mendes-Santos, Tiago, Paiva, Thereza, Santos, Raimundo R. dos, and Scalettar, Richard T.. Ferromagnetism beyond Lieb's theorem. United States: N. p., Web. doi:10.1103/PhysRevB.94.155107.
Costa, Natanael C., Mendes-Santos, Tiago, Paiva, Thereza, Santos, Raimundo R. dos, & Scalettar, Richard T.. Ferromagnetism beyond Lieb's theorem. United States. doi:10.1103/PhysRevB.94.155107.
Costa, Natanael C., Mendes-Santos, Tiago, Paiva, Thereza, Santos, Raimundo R. dos, and Scalettar, Richard T.. 2016. "Ferromagnetism beyond Lieb's theorem". United States. doi:10.1103/PhysRevB.94.155107. https://www.osti.gov/servlets/purl/1477007.
@article{osti_1477007,
title = {Ferromagnetism beyond Lieb's theorem},
author = {Costa, Natanael C. and Mendes-Santos, Tiago and Paiva, Thereza and Santos, Raimundo R. dos and Scalettar, Richard T.},
abstractNote = {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, 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 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.},
doi = {10.1103/PhysRevB.94.155107},
journal = {Physical Review B},
number = 15,
volume = 94,
place = {United States},
year = {2016},
month = {10}
}