Stability of Ferromagnetism in the Hubbard Model on the Kagome Lattice

Tanaka, Akinori; Ueda, Hiromitsu

doi:10.1103/physrevlett.90.067204

Cited by 72 publications

(75 citation statements)

References 12 publications

(13 reference statements)

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“…From a tight-binding perspective (Fig. 40a), in addition to two strongly dispersive bands identical to the honeycomb band structure, the kagome Hubbard model features one flat band which, for appropriate fillings, has been suggested to be particularly susceptible to ferromag- netism along Stoner's criterion [218]. Aside from that, however, the pure view from Fermi surface topology on the dispersive kagome band would suggest an identical profile of Fermi surface instabilities in the kagome Hubbard model as compared to the honeycomb Hubbard model in Sec.…”

Section: Sublattice Interference: Kagome Vs Honeycomb Latticementioning

confidence: 99%

Functional renormalization group for multi-orbital Fermi surface instabilities

Platt

Hanke

Thomale

2013

Advances in Physics

192

253

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Technological progress in material synthesis, as well as artificial realization of condensed matter scenarios via ultra-cold atomic gases in optical lattices or epitaxial growth of thin films, is opening the gate to investigate a plethora of unprecedented strongly correlated electron systems. In a large subclass thereof, a metallic state of layered electrons undergoes an ordering transition below some temperature into unconventional states of matter driven by electronic correlations, such as magnetism, superconductivity, or other Fermi surface instabilities. While this type of phenomena has been a well-established direction of research in condensed matter for decades, the variety of today's accessible scenarios pose fundamental new challenges to describe them. A core complication is the multi-orbital nature of the low-energy electronic structure of these systems, such as the multi-d orbital nature of electrons in iron pnictides and transition-metal oxides in general, but also electronic states of matter on lattices with multiple sites per unit cell such as the honeycomb or kagome lattice. In this review, we propagate the functional renormalization group (FRG) as a suited approach to investigate multi-orbital Fermi surface instabilities. The primary goal of the review is to describe the FRG in explicit detail and render it accessible to everyone both at a technical and intuitive level. Summarizing recent progress in the field of multi-orbital Fermi surface instabilities, we illustrate how the unbiased fashion by which the FRG treats all kinds of ordering tendencies guarantees an adequate description of electronic phase diagrams and often allows to obtain parameter trends of sufficient accuracy to make qualitative predictions for experiments. This review includes detailed and illustrative illustrations of magnetism and, in particular, superconductivity for the iron pnictides from the viewpoint of FRG. Furthermore, it discusses candidate scenarios for topological bulk singlet superconductivity and exotic particle-hole condensates on hexagonal lattices such as sodium-doped cobaltates, graphene doped to van Hove filling, and the kagome Hubbard model. In total, the FRG promises to be one of the most versatile and revealing numerical approaches to address unconventional Fermi surface instabilities in future fields of condensed matter research.

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Section: Sublattice Interference: Kagome Vs Honeycomb Latticementioning

confidence: 99%

Functional renormalization group for multi-orbital Fermi surface instabilities

Platt

Hanke

Thomale

2013

Advances in Physics

192

253

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“…x,σâx,σ terms toĤ , it is possible to prove the same statement for sufficiently large U and s. The proof uses techniques similar to that in [10][11][12][13][14]. 5 The checkerboard lattice is a d-dimensional extension of the face centered cubic lattice, whose lattice points are given by (x 1 , x 2 , .…”

Section: Theorem 3 Suppose That the Electron Number Nmentioning

confidence: 96%

“…Important examples include special classes of the Hubbard model with a dispersionless band (flat-band ferromagnetism) introduced by Mielke [6,7] and by Tasaki [8,9], and some models obtained by modifying the flat-band models [10][11][12][13][14]. The latter examples are of special importance since they provide rigorous examples of itinerant ferromagnetism in many-electron models without any singularities.…”

Section: Introductionmentioning

confidence: 98%

Metallic Ferromagnetism Supported by a Single Band in a Multi-band Hubbard Model

Tanaka

Tasaki

2016

J Stat Phys

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We construct a multi-band Hubbard model on the lattice obtained by "decorating" a closely packed d-dimensional lattice M (such as the triangular lattice) where d ≥ 2. We take the limits in which the Coulomb interaction and the band gap become infinitely large. Then there remains only a single band with finite energy, on which electrons are supported. Let the electron number be N e = |M| − N h , where |M| corresponds to the electron number which makes the lowest (finite energy) band half-filled, and N h is the number of "holes". It is expected that the model exhibits metallic ferromagnetism if N h /|M| is nonvanishing but sufficiently small. We prove that the ground states exhibit saturated ferromagnetism if N h ≤ (const.)|M| 2/(d+2) , and exhibit (not necessarily saturated) ferromagnetism if N h ≤ (const.)|M| (d+1)/(d+2) . This may be regarded as a rigorous example of metallic ferromagnetism provided that the system size |M| is not too large.

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“…Tasaki has proved that the saturated ferromagnetism is stable against a perturbation which bends the electron band [10]. Tanaka and Ueda have shown the stability of the saturated ferromagnetism in a more complicated two-dimensional model in Mielke's class [11]. The ferromagnetism in flat-band Hubbard models and their perturbed models is believed to be one universal nature of ferromagnetism in many-electron systems.…”

Section: Introductionmentioning

confidence: 99%

Ferromagnetic Domain Wall and Spiral Ground States in One-Dimensional Deformed Flat-Band Hubbard Model

Homma

Itoi

2004

Journal of Statistical Physics

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We construct a set of exact ground states with a localized ferromagnetic domain wall and an extended spiral structure in a quasi-one-dimensional deformed flatband Hubbard model. In the case of quarter filling, we show the uniqueness of the ground state with a fixed magnetization. The ground states with these structures are degenerate with the all-spin-up and all-spin-down states. This property of the degeneracy is the same as the domain wall solutions in the XXZ Heisenberg-Ising model. We derive a useful recursion relation for the normalization of the domain wall ground state. Using this recursion relation, we discuss the convergence of the ground state expectation values of arbitrary local operators in the infinite-volume limit. In the ground state of the infinite-volume system, the translational symmetry is spontaneously broken by this structure. We prove that the cluster property holds for the domain wall ground state and excited states. We also estimate bounds of the ground state expectation values of several observables, such as one-and two-point functions of spin and electron number density. keywords: ferromagnetic domain wall, spiral state, flat-band Hubbard model, exact solution, quantum effect, cluster property

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Stability of Ferromagnetism in the Hubbard Model on the Kagome Lattice

Cited by 72 publications

References 12 publications

Functional renormalization group for multi-orbital Fermi surface instabilities

Functional renormalization group for multi-orbital Fermi surface instabilities

Metallic Ferromagnetism Supported by a Single Band in a Multi-band Hubbard Model

Ferromagnetic Domain Wall and Spiral Ground States in One-Dimensional Deformed Flat-Band Hubbard Model

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