We present an extension of the cell-construction method for the flat-band ferromagnetism. In a rather general setting, we construct Hubbard models with highly degenerate single-electron ground states and obtain a formal representation of these single-electron ground states. By our version of the cell-construction method, various types of flat-band Hubbard models, including the one on line graphs, can be designed and shown to have the unique ferromagnetic ground states when the electron number is equal to the degeneracy of the single-electron ground states.
In narrow-band systems, correlated contribution to effective hopping becomes important, and one needs to carefully consider three types of hopping processes: between doubly and singly occupied sites, between singly occupied and empty sites, and between doubly occupied and empty or two singly occupied sites. All three hopping parameters cannot vanish simultaneously, and one should specify for which of these processes the band becomes flat. By means of exact diagonalization of finite systems we demonstrate that three hoppings play qualitatively different roles in many-body effects, in particular…
We discuss twisted bilayer graphene (TBG) based on a theorem of flat band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single particle density matrix of the flat band states is irreducible and we argue that this result can be applied to the quasi-flat bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle $θ\sim1.05^\circ$. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG ($n=0$). We then show that the theorem can also…
We study the spin-1 excitation spectra of the flatband ferromagnetic phases in interacting topological insulators. As a paradigm, we consider a quarter filled square lattice Hubbard model whose free part is the $π$ flux state with topologically nontrivial and nearly-flat electron bands, which can realize either the Chern or $Z_2$ Hubbard model. By using the numerical exact diagonalization method with a projection onto the nearly-flat band, we obtain the ferromagnetic spin-1 excitation spectra for both the Chern and $Z_2$ Hubbard models, consisting of spin waves and Stoner continuum. The spectr…
Interaction-driven spin polaron in itinerant flat-band ferromagnetism
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固态微结构国家重点实验室和物理学院）；School of Physics, Nanjing University of Science and Technology（南京理工大学物理学院）；Jiangsu Physical Science Research Center（江苏省物理科学研究中心）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University（南京大学江苏省量子信息科学与技术重点实验室）
Many graphene moiré superlattices host narrow bands with non-zero valley Chern numbers. We provide analytical and numerical evidence for a robust spin and/or valley polarized insulator at total integer band filling in nearly flat bands of several different moiré materials. In the limit of a perfectly flat band, we present analytical arguments in favor of the ferromagnetic state substantiated by numerical calculations. Further, we numerically evaluate its stability for a finite bandwidth. We provide exact diagonalization results for models appropriate for ABC trilayer graphene aligned with hBN,…
Several moiré systems created by various twisted bilayers have manifested magnetism under flatband conditions leading to enhanced interaction effects. We theoretically study stability of moiré flatband ferromagnetism against collective excitations, with a focus on the effects of Bloch band quantum geometry. The spin magnon spectrum is calculated using different approaches, including Bethe-Salpeter equation, single mode approximation, and an analytical theory. One of our main results is an analytical expression for the spin stiffness in terms of the Coulomb interaction potential, the Berry curv…
Linear Ensemble-Constrained Quantum Monte Carlo: From Dilute Fermi Gas to Flat-Band Ferromagnetism
Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education) School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院人工结构量子控制教育部重点实验室）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Hefei National Laboratory（合肥国家实验室）
We present rigorous results for the SU($n$) Fermi-Hubbard model on the railroad-trestle lattice. We first study the model with a flat band at the bottom of the single-particle spectrum and prove that the ground states exhibit SU($n$) ferromagnetism when the total fermion number is the same as the number of unit cells. We then perturb the model by adding extra hopping terms and make the flat band dispersive. Under the same filling condition, it is proved that the ground states of the perturbed model remain SU($n$) ferromagnetic when the bottom band is nearly flat. This is the first rigorous exa…
We present rigorous results for the SU($n$) Fermi-Hubbard models with finite-range hopping in $d$ ($\ge 2$) dimensions. The models are defined on a class of decorated lattices. We first study the models with flat bands at the bottom of the single-particle spectrum and prove that the ground states exhibit SU($n$) ferromagnetism when the number of particles is equal to the number of unit cells. We then perturb the models by adding particular hopping terms and make the bottom bands dispersive. Under the same filling condition, it is proved that the ground states remain SU($n$) ferromagnetic when …
We investigate the para-ferro transition of the repulsive SU($N$) Hubbard model on one- and two-dimensional Tasaki lattices. Under certain restrictions for constructing localized many-particle ground states of flat-band ferromagnetism, the quantum strongly correlated electrons model is mapped to a classical statistical geometric site-percolation problem, where the nontrivial weights of different configurations must be considered. We prove rigorously the para-ferro transition for the SU($N$) Hubbard model on one-dimensional Tasaki lattice by transfer-matrix method, and numerically verify it for…
Whether spin-independent Coulomb interaction in an electron system can be the origin of ferromagnetism has been an open problem for a long time. Recently, a "constructive" approach to this problem has been developed, and the existence of ferromagnetism in the ground states of certain Hubbard models was established rigorously. A special feature of these Hubbard models is that their lowest bands (in the corresponding single-electron problems) are completely flat. Here we study models obtained by adding small but arbitrary translation-invariant perturbation to the hopping Hamiltonian of these fla…
We study the quantum phase diagram of spinful fermions on kagome lattice with half-filled lowest flat bands. To understand the competition between magnetism, flat band frustration, and repulsive interactions, we adopt an extended $t$-$J$ model, where the hopping energy $t$, antiferromagnetic Heisenberg interaction $J$, and short-range neighboring Hubbard interaction $V$ are considered. In the weak $J$ regime, we identify a fully spin-polarized phase, which can further support the spontaneous Chern insulating phase driven by the short-range repulsive interaction. This phase still emerges with i…
Interaction in a flat band is magnified due to the divergence in the density of states, which gives rise to a variety of many-body phenomena such as ferromagnetism and Wigner crystallization. Until now, however, most studies of the flat band physics are based on model systems, making their experimental realization a distant future. Here, we propose a class of systems made of real atoms, namely, carbon atoms with realistic physical interactions (dubbed here as Kagome graphene/graphyne). Density functional theory calculations reveal that these Kagome lattices offer a controllable way to realize …
We study the flat-band ferromagnetic phase of the Haldane-Hubbard model on a honeycomb lattice within a bosonization scheme for flat-band Chern insulators, focusing on the calculation of the spin-wave excitation spectrum. We consider the Haldane-Hubbard model with the noninteracting lower bands in a nearly-flat band limit, previously determined for the spinless model, and at 1/4-filling of its corresponding noninteracting limit. Within the bosonization scheme, the Haldane-Hubbard model is mapped into an effective interacting boson model, whose quadratic term allows us to determine the spin-wav…
We study the flat-band ferromagnetic phase of a spinfull and time-reversal symmetric Haldane-Hubbard model on a honeycomb lattice within a bosonization formalism for flat-band Z$_2$ topological insulators. Such a study extend our previous one [L. S. G. Leite and R. L. Doretto, Phys. Rev. B {\bf 104}, 155129 (2021)] concerning the flat-band ferromagnetic phase of a correlated Chern insulator described by a Haldane-Hubbard model. We consider the topological Hubbard model at $1/4$ filling of its corresponding noninteracting limit and in the nearly flat band limit of its lower free-electronic band…
Recently, a SU(4) $π$-flux Hubbard model on the honeycomb lattice has been proposed to study the spin-orbit excitations of $α$-ZrCl$_3$ [Phys.~Rev.~Lett. 121.097201~(2017)]. Based on this model with a zigzag edge, we show the edge defects can induce edge flat bands that result in a SU(4) edge ferromagnetism. We develop an effective one-dimensional interaction Hamiltonian to study the corresponding SU(4) spin excitations. Remarkably, SU(4) spin excitations of the edge ferromagnet appear as a continuum covering the entire energy region rather than usual magnons. Through further entanglement entr…
Since its introduction in 1963, the Hubbard model has becomes one of the most popular models used in the literature to study cooperative phenomena in narrow-band metals (ferromagnetism, metal-insulator transitions, charge-density waves, high-T$_c$ superconductivity). Amongst all these cooperative phenomena, the problem of itinerant ferromagnetism in the Hubbard model has the longest history. However, in spite of an impressive research activity in the past, the underlying physics (microscopic mechanisms) that leads to the stabilization of itinerant ferromagnetism in Hubbard model (narrow-band m…
Strongly interacting fermionic systems host a variety of interesting quantum many-body states with exotic excitations. For instance, the interplay of strong interactions and the Pauli exclusion principle can lead to Stoner ferromagnetism, but the fate of this state remains unclear when kinetic terms are added. While in many lattice models the fermions' dispersion results in delocalization and destabilization of the ferromagnet, flat bands can restore strong interaction effects and ferromagnetic correlations. To reveal this interplay, here we propose to study the Hofstadter-Fermi-Hubbard model …
