Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons

Abstract

In this review we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. Main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki-Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems. Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.

arXiv comment72 pages, 20 figures, 157 references; accepted for publication in International Journal of Modern Physics B

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Cited by in corpus (158)

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• Classification of flat bands according to the band-crossing singularity of Bloch wave functions
• Compact localized states and flatband generators in one dimension
• Non-Bloch band collapse and chiral Zener tunneling
• Chiral Flat Bands: Existence, Engineering and Stability
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Localization of weakly disordered flat band states
• Disorder-Free Localization and Many-Body Quantum Scars from Magnetic Frustration
• Magnetism of the N=42 kagome lattice antiferromagnet
• Landau-Zener Bloch oscillations with perturbed flat bands
• Flat bands in lattices with non-Hermitian coupling
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• Scattering matrix invariants of Floquet topological insulators
• Universal $d=1$ flatband generator from compact localized states
• Flatband generator in two dimensions
• Crystal Net Catalog of Model Flat Band Materials
• Flat band superconductivity in the square-octagon lattice
• Magnon crystallization in the kagome lattice antiferromagnet
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• Band flatness optimization through complex analysis
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• Nonlinear localized flatband modes with spin-orbit coupling
• Nonlinear symmetry breaking of Aharonov-Bohm cages
• Electron-Phonon Interactions in Flat Band Systems
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• Interplay of disorder and interactions in a flat-band supporting diamond chain
• Designing flat-band tight-binding models with tunable multifold band touching points
• Anatomy of Topological Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices
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• Flat-band-based multifractality in the all-band-flat diamond chain
• Are Heavy Fermion Strange Metals Planckian?
• Compact Discrete Breathers on Flat Band Networks
• Quantum network transfer and storage with compact localized states induced by local symmetries
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• Topology and localization of a periodically driven Kitaev model
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• Flat band transport and Josephson effect through a finite-size sawtooth lattice
• Delta chain with anisotropic ferromagnetic and antiferromagnetic interactions
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• Engineering slow light and mode crossover in a fractal-kagome waveguide network
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• Observation of Flat Bands and Dirac Cones in a Pyrochlore Lattice Superconductor
• Flat-band spin dynamics and phonon anomalies of the saw-tooth spin-chain system Fe${}_2$O(SeO${}_3$)${}_2$
• Kondo Breakdown via Fractionalization in a Frustrated Kondo Lattice Model
• Compactly Supported Wannier Functions and Strictly Local Projectors
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• Metal-insulator transition in infinitesimally weakly disordered flatbands
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• Wannier-Stark flatbands in Bravais lattices
• Excitation of localized condensates in the flat band of exciton-polariton Lieb lattice
• Ferrimagnetism in delta chain with anisotropic ferromagnetic and antiferromagnetic interactions
• Many-body localization transition from flatband fine-tuning
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• Phase separated magnetic ground state in Mn${}_3$Ga${}_{0.45}$Sn${}_{0.55}$C
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• Honeycomb-Lattice Mott insulator on Tantalum Disulphide
• Frustration-induced supersolids in the absence of inter-site interactions
• Stopping and reversing sound via dynamic dispersion tuning in a phononic metamaterial
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• Heisenberg-Ising delta-chain with bond alternation
• Frustrated polaritons
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• Two-dimensional spin models with macroscopic degeneracy
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• Selective band interaction and long-range hopping in a structured environment with giant atoms
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• Magnetic properties of ferro-antiferromagnetic spin triangle chain
• Flat band mediated photon-photon interactions in 2D waveguide QED networks
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