Ferromagnetism in the Hubbard model with topological/non-topological flat bands

Katsura, Hosho; Maruyama, Isao; Tanaka, Akinori; Tasaki, Hal

doi:10.1209/0295-5075/91/57007

Cited by 87 publications

(86 citation statements)

References 43 publications

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“…The origin of these flat bands can be clarified by the factorization of the Hamiltonian (3), as was done for the tight-binding model on complete graphs [28]. To this aim, we rewrite the Hamiltonian (3) as…”

Section: Origin Of the Flat Bandsmentioning

confidence: 99%

Flat bands and Dirac cones in breathing lattices

Essafi

Jaubert

Udagawa

2017

J. Phys.: Condens. Matter

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Abstract. In breathing pyrochlores and kagomes, couplings between neighbouring tetrahedra and triangles are free to differ. Breathing lattices thus offer the possibility to explore a different facet of the rich physics of these systems. Here we consider nearest-neighbour classical Heisenberg interactions, both ferromagnetic and antiferromagnetic, and study how the anisotropy of breathing lattices modifies the mode spectrum of pyrochlore and kagome systems. The nature and degeneracy of the flat bands are shown to be preserved for any value of the anisotropy. These flat bands can coexist with Dirac nodes at the Γ point when the model becomes particle-hole symmetric. We also derive the nature of the ground state for the breathing kagome lattice, which bears a spontaneous chirality when neighbouring triangles are alternatively ferromagnetic and antiferromagnetic.

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Section: Origin Of the Flat Bandsmentioning

confidence: 99%

Flat bands and Dirac cones in breathing lattices

Essafi

Jaubert

Udagawa

2017

J. Phys.: Condens. Matter

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“…selected external magnetic field values) emerges without any restriction regarding the non-interacting Hamiltonian parameter values. Such a behavior is rare, but has been previously observed for other chains as well [22], being important also in the study of the topological classification of electron systems [26].…”

Section: The Deduced Ground Statesmentioning

confidence: 85%

Exact ground states for polyphenylene type of hexagon chains

et al. 2011

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This article is dedicated to Dieter Vollhardt on the occasion of his 60th birthday.A technique based on positive semidefinite operator properties has been used in deducing exact ground states for hexagon chains of polyphenylene type (hexagons interconnected by bonds build up the 1D periodic structure), placed in a constant external magnetic field B perpendicular to the surface containing the system. The used Hubbard type of model takes into account B by Peierls phase factors, and has the peculiar property to provide only flat bands in the bare band structure for elevated external field values independent on the parameters entering in the kinetic part of the Hamiltonian. The deduced ground states are non-magnetic or ferromagnetic in character, localized in the thermodynamic limit, and besides the fact that B is able to switch the system between different phases, emphasize that the localization length and connectivity conditions can be tuned by external magnetic fields.

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“…Our work opens up a possibility of investigating manybody physics inside a QZ subspace, which can naturally be made flat [36][37][38]. With tunable interaction [69], ultracold atoms provide an ideal platform for experimental implementation.…”

Section: Arxiv:161108164v2 [Quant-ph] 26 Apr 2017mentioning

confidence: 99%

Zeno Hall Effect

2017

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We show that the quantum Zeno effect gives rise to the Hall effect by tailoring the Hilbert space of a two-dimensional lattice system into a single Bloch band with a nontrivial Berry curvature. Consequently, a wave packet undergoes transverse motion in response to a potential gradient -a phenomenon we call the Zeno Hall effect to highlight its quantum Zeno origin. The Zeno Hall effect leads to retroreflection at the edge of the system due to an interplay between the band flatness and the nontrivial Berry curvature. We propose an experimental implementation of this effect with ultracold atoms in an optical lattice.Introduction.-The state-of-the-art experimental techniques in atomic, molecular and optical physics have made it possible not only to engineer the Hamiltonian of a quantum system, but also to control its interaction with the environment [1][2][3][4][5][6]. Here controlled dissipation can serve as a resource for quantum coherence and entanglement [7,8], with versatile applications to quantumstate preparation [9][10][11], quantum computation [12] and quantum simulation [13,14].The experimental progress in turn has stimulated theoretical studies in open quantum systems [15][16][17][18], such as the Hall effects in the presence of dissipation [19][20][21][22]. It has been shown that the quantization of the transverse conductivity in the integer quantum Hall regime is robust against dissipation [19,22], while a nontrivial influence of dissipation emerges for the fractional quantum Hall effect [20] and the anomalous Hall effect [21].In this Letter, we point out yet another Hall effect in open quantum systems -the Hall effect due to dissipation. This differs fundamentally from the previous works in that the Hall effect originates from the interaction with the environment instead of the bare HamiltonianĤ of the system. Our idea is based on two key ingredients: (i) to use dissipation to tailor the accessible Hilbert space S and hence to change the effective Hamiltonian (see Fig. 1 (a)) [23][24][25]; (ii) the noncommutativity of position operators in a constrained Bloch band with a nontrivial Berry curvature [26]. (i) exploits the quantum Zeno (QZ) effect [27][28][29], which is well studied in the context of quantum measurement [30,31] and occurs also for strong dissipation [32-34] as a continuous limit of repeated measurements [23]. (ii) shares the same physics behind the anomalous Hall effect [35]. As schematically illustrated in Figs. 1 (b) and (c), if the entire Hilbert space is tailored into a single Bloch band with a nonzero Berry curvature, a wave packet undergoes transverse motion even ifĤ has no kinetics term. We call such a phenomenon the Zeno Hall effect (ZHE). Our scheme is readily applicable to create a flat band with a tunable Berry curvature, and thus provides an ideal platform to explore quantum many-body physics [36][37][38]. Surprisingly, the wave-packet dynamics in such a flat band is

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Ferromagnetism in the Hubbard model with topological/non-topological flat bands

Cited by 87 publications

References 43 publications

Flat bands and Dirac cones in breathing lattices

Flat bands and Dirac cones in breathing lattices

Exact ground states for polyphenylene type of hexagon chains

Zeno Hall Effect

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