Flat-band ferromagnetism in extended Δ-chain Hubbard models

Ichimura, Michio; Kusakabe, Koichi; Watanabe, Shinji; Onogi, T.

doi:10.1103/physrevb.58.9595

Cited by 19 publications

(34 citation statements)

References 12 publications

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“….. Note that the dimer mapping can be applied to other one-dimensional models like a model originally due to Watanabe [4] or two kagome-like chains [7].…”

Section: Models With Localized Electron Statesmentioning

confidence: 99%

“…In particular, on highly frustrated lattices it is possible to construct a macroscopic number of ground states (GSs) using localized singleparticle excitations as building blocks. On the one hand, such a construction has been applied to the so-called flatband Hubbard models in order to show that they exhibit fully saturated ferromagnetism for suitable electron fillings (see, e.g., [1][2][3][4][5]). On the other hand, so-called localized magnon states have been found to yield exact many-body GSs for highly frustrated quantum antiferromagnets in high magnetic fields [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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Ground-state degeneracy and low-temperature thermodynamics of correlated electrons on highly frustrated lattices

Honecker¹,

Derzhko²,

Richter³

2009

Physica B: Condensed Matter

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Highly frustrated lattices yield a completely flat lowest single-electron band. Remarkably, exact many-body ground states can be constructed for the repulsive Hubbard model and the t − J model by filling this flat band with localized electron states. This construction leads to a macroscopic ground-state degeneracy. We discuss how to compute these ground-state degeneracies for a certain class of models, including in particular the sawtooth chain. Furthermore, we discuss generic consequences for lowtemperature thermodynamic properties, like the appearance of a low-temperature peak in the specific heat. Finally, we present complementary numerical results obtained by exact diagonalization. (A. Honecker). ( †)i,σ are the usual fermion operators, n i,σ = c † i,σ c i,σ , n i = n i,↑ + n i,↓ . U ≥ 0 is the on-site Coulomb repulsion. Note that we have chosen [17] non-standard sign conventions for the hopping integrals t i,j and the chemical potential µ in order to emphasize the analogy with the antiferromagnetic Heisenberg model in a magnetic field.Secondly, we consider the t − J model with Hamiltonian

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“….. Note that the dimer mapping can be applied to other one-dimensional models like a model originally due to Watanabe [4] or two kagome-like chains [7].…”

Section: Models With Localized Electron Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ground-state degeneracy and low-temperature thermodynamics of correlated electrons on highly frustrated lattices

Honecker¹,

Derzhko²,

Richter³

2009

Physica B: Condensed Matter

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“…Although the rigorous proof on flat-band magnetism by Mielke and Tasaki 8 is not applicable to the partially flat band of the Ga wire because the band is not completely flat, it is shown that the ground state is ferromagnetic when electron-electron repulsion energy or the Hubbard U is larger than a certain threshold value (ϳ0.4 eV), by exact diagonalization calculation on the basis of a minimal tight-binding model for the Ga wire. 9 As shown above, atomic wires adsorbed on the semiconductor surface can exhibit a wide variety of properties. However, to date there is no theoretical guiding principle to design conductive or ferromagnetic atomic wires.…”

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confidence: 93%

First-principles calculation of As atomic wires on a H-terminated Si(100) surface

et al. 1999

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The atomic and electronic structures of As atomic wires, which are formed by As adsorbates around a dangling-bond wire on a H-terminated Si͑100͒, are investigated by using first-principles calculations within the local-density-functional approach. By comparing the metastable geometries of the As atomic wires with those of the Ga atomic wires previously studied, we found that As atoms have a stronger tendency to form covalent bonds. Interestingly, the most stable As configuration has an energy band with no significant dispersion as the lowest empty surface state. Electron-doping into this flat band may open up the possibility to form a ferromagnetic atomic wire. To exemplify such doping, we show that a half-filled flat band can be realized, its flatness unchanged, when K adsorbates are supplied to the As wire.

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“…We expect that the t2J model with weak J i;j has the same localized excitations as the repulsive Hubbard model such that it shares in particular the same properties with respect to flat-band ferromagnetism [9][10][11][12][13]. The main advantage of the t2J model is a substantially reduced Hilbert space dimension close to n ¼ 1 which simplifies a full diagonalization and thus the exact determination of finite-temperature properties of a finite system.…”

mentioning

confidence: 96%

“…Recently, we have pointed out [8] analogies to flat-band ferromagnetism in the Hubbard model on the same lattices (see e.g. [9][10][11][12][13]). …”

mentioning

confidence: 99%

Enhanced low-temperature entropy and flat-band ferromagnetism in the model on the sawtooth lattice

Honecker¹,

Richter²

2007

Journal of Magnetism and Magnetic Materials

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Using the example of the sawtooth chain, we argue that the t2J model shares important features with the Hubbard model on highly frustrated lattices. The lowest single-fermion band is completely flat (for a specific choice of the hopping parameters t i;j in the case of the sawtooth chain), giving rise to single-particle excitations which can be localized in real space. These localized excitations do not interact for sufficient spatial separations such that exact many-electron states can also be constructed. Furthermore, all these excitations acquire zero energy for a suitable choice of the chemical potential m. This leads to: (i) a jump in the particle density at zero temperature, (ii) a finite zero-temperature entropy, (iii) a ferromagnetic ground state with a charge gap when the flat band is fully occupied and (iv) unusually large temperature variations when m is varied adiabatically at finite temperature. r During the past years, it has been noted that exact ground states can be constructed for the antiferromagnetic XXZ model at high fields on a large class of highly frustrated lattices (see [1][2][3] and references therein). This leads to a finite zero-temperature entropy exactly at the saturation field and an enhanced magnetocaloric effect [2,4-6], suggesting potential applications for efficient low-temperature magnetic refrigeration [4,7]. Recently, we have pointed out [8] analogies to flat-band ferromagnetism in the Hubbard model on the same lattices (see e.g. [9][10][11][12][13]).Here, we will illustrate some of the issues with exact diagonalization results for the t2J model. The t2J model arises as the large-U limit of the Hubbard model and is defined by the Hamiltonian H ¼ X s

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Flat-band ferromagnetism in extended Δ-chain Hubbard models

Cited by 19 publications

References 12 publications

Ground-state degeneracy and low-temperature thermodynamics of correlated electrons on highly frustrated lattices

Ground-state degeneracy and low-temperature thermodynamics of correlated electrons on highly frustrated lattices

First-principles calculation of As atomic wires on a H-terminated Si(100) surface

Enhanced low-temperature entropy and flat-band ferromagnetism in the model on the sawtooth lattice

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