Hubbard models with nearly flat bands: Ground-state ferromagnetism driven by kinetic energy

Abstract

We consider the standard repulsive Hubbard model with a flat lowest-energy band for two one-dimensional lattices (diamond chain and ladder) as well as for a two-dimensional lattice (bilayer) at half filling of the flat band. The considered models do not fall in the class of Mielke-Tasaki flat-band ferromagnets, since they do not obey the connectivity conditions. However, the ground-state ferromagnetism can emerge, if the flat band becomes dispersive. To study this kinetic-energy-driven ferromagnetism we use perturbation theory and exact diagonalization of finite lattices. We find as a typical scenario that small and moderate dispersion may lead to a ferromagnetic ground state for sufficiently large on-site Hubbard repulsion $U>U_c$, where $U_c$ increases monotonically with the acquired bandwidth. However, we also observe for some specific parameter cases, that (i) ferromagnetism appears at already very small $U_c$, (ii) ferromagnetism does not show up at all, (iii) the critical on-site repulsion $U_c$ is a nonmonotonic function of the bandwidth, or that (iv) a critical bandwidth is needed to open the window for ground-state ferromagnetism.

arXiv comment22 pages, 11 figures

References in corpus (28)

• From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
• Band touching from real space topology in frustrated hopping models
• Ferromagnetism in the Hubbard Model-- Examples from Models with Degenerate Single-Electron Ground States
• Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
• Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
• Bose condensation in flat bands
• Detangling Flat Bands into Fano Lattices
• Flat Bands Under Correlated Perturbations
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Multi-step approach to microscopic models for frustrated quantum magnets - the case of the natural mineral azurite
• Ferromagnetism in Hubbard Models
• Anisotropic two-dimensional electron gas at SrTiO3(110) protected by its native overlayer
• Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem
• Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices
• Ferromagnetism in single-band Hubbard models with a partially flat band
• Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
• SNEG - Mathematica package for symbolic calculations with second-quantization-operator expressions
• Ferromagnetism in the Hubbard model: A constructive approach
• Stability of Ferromagnetism in Hubbard models with degenerate single-particle ground states
• Robust flat bands in RCo5 (R=rare earth) compounds
• Exact low-temperature properties of a class of highly frustrated Hubbard models
• Hubbard Model on Decorated Lattices
• The square-kagome quantum Heisenberg antiferromagnet at high magnetic fields: The localized-magnon paradigm and beyond
• Localized states on triangular traps and low-temperature properties of the antiferromagnetic Heisenberg and repulsive Hubbard models
• The spin 1/2 Heisenberg star with frustration II: The influence of the embedding medium
• Dispersion-driven ferromagnetism in a flat-band Hubbard system
• Reversible first-order transition in Pauli percolation
• Flat band ferromagnetism without connectivity conditions in the flat band

Cited by in corpus (8)

• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets
• Flat bands and compactons in mechanical lattices
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Ground state spin and excitation energies in half-filled Lieb lattices
• Identifying Instabilities with Quantum Geometry in Flat Band Systems
• Phase diagram of a coupled trimer system at half filling using the Hubbard model