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.

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

References in corpus (21)

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• Bose condensation in flat bands
• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Anderson localisation in tight-binding models with flat bands
• Magnetocaloric effect in one-dimensional antiferromagnets
• Nature of the spin dynamics and 1/3 magnetization plateau in azurite
• Impurity and correlation effects on transport in one-dimensional quantum wires
• Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem
• Dynamic and thermodynamic properties of the generalised diamond chain model for azurite
• Linear independence of localized magnon states
• Ferromagnetism in armchair graphene nanoribbon
• Almost Perfect Frustration in the Dimer Magnet Ba${}_2$CoSi${}_2$O${}_6$Cl${}_2$
• Exact low-temperature properties of a class of highly frustrated Hubbard models
• Flat band analogues and flux driven extended electronic states in a class of geometrically frustrated fractal networks
• There are no Goldstone bosons on the Bethe lattice
• Ensemble inequivalence in random graphs
• Flat bands in Weaire-Thorpe model and silicene
• Low-energy behaviour of strongly-interacting bosons on a flat-banded lattice above the critical filling factor
• Frustrated diamond-chain quantum $XXZ$ Heisenberg antiferromagnet in a magnetic field
• Dispersion-driven ferromagnetism in a flat-band Hubbard system
• Semiquantitative theory for high-field low-temperature properties of a distorted diamond spin chain

Cited by in corpus (101)

• Chiral Flat Bands: Existence, Engineering and Stability
• Effective theory and emergent $SU(2)$ symmetry in the flat bands of attractive Hubbard models
• Flatband generator in two dimensions
• Crystal Net Catalog of Model Flat Band Materials
• Topological flat Wannier-Stark bands
• Nonlinear localized flatband modes with spin-orbit coupling
• Designing flat-band tight-binding models with tunable multifold band touching points
• Critical-to-Insulator Transitions and Fractality Edges in Perturbed Flatbands
• Thermodynamics of the spin-half square-kagome lattice antiferromagnet
• Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices
• Flat-band-based multifractality in the all-band-flat diamond chain
• Are Heavy Fermion Strange Metals Planckian?
• Topology and localization of a periodically driven Kitaev model
• Thermodynamic properties of Ba${}_2$CoSi${}_2$O${}_6$Cl${}_2$ in strong magnetic field: Realization of flat-band physics in a highly frustrated quantum magnet
• Fast quantum transfer mediated by topological domain walls
• Thermodynamics of delta-chain with ferro- and antiferromagnetic interactions
• Flat-band physics in the spin-1/2 sawtooth chain
• Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice
• 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${}_3$)${}_2$
• Frustrated magnetism of spin-1/2 Heisenberg diamond and octahedral chains as a statistical-mechanical monomer-dimer problem
• Metal-insulator transition in infinitesimally weakly disordered flatbands
• Electric field driven flat bands: Enhanced magnetoelectric and electrocaloric effects in frustrated quantum magnets
• Many-body localization transition from flatband fine-tuning
• Ferrimagnetism in delta chain with anisotropic ferromagnetic and antiferromagnetic interactions
• Magnetism of the $s=1/2$ $J_1$-$J_2$ square-kagome lattice antiferromagnet
• Frustrated honeycomb-lattice bilayer quantum antiferromagnet in a magnetic field: Unconventional phase transitions in a two-dimensional isotropic Heisenberg model
• Phase separated magnetic ground state in Mn${}_3$Ga${}_{0.45}$Sn${}_{0.55}$C
• Honeycomb-Lattice Mott insulator on Tantalum Disulphide
• Probing Flat Band Physics in Spin Ice Systems via Polarized Neutron Scattering
• Single and double linear and nonlinear flatband chains: spectra and modes
• Melting of magnetization plateaus for kagome and square-kagome lattice antiferromagnets
• Flat Band Induced Metal-Insulator Transitions for Weak Magnetic Flux and Spin-Orbit Disorder
• The delta-chain with ferro- and antiferromagnetic interactions in applied magnetic field
• Kondo-lattice-mediated interactions in flat band systems
• Anti-$\mathcal{P}\mathcal{T}$ flatbands
• Persistence of the flat band in a kagome magnet with dipolar interactions
• Designer quantum states on a fractal substrate: compact localization, flat bands and the edge modes
• Unconventional delocalization in a family of 3D Lieb lattices
• Multiple flat bands and localized states in photonic super-Kagome lattices
• Conductance transition with interacting bosons in an Aharonov-Bohm cage
• Coupled frustrated ferromagnetic and antiferromagnetic quantum spin chains in the quasi-one-dimensional mineral antlerite, Cu${}_3$SO${}_4$(OH)${}_4$
• Correlation functions and characteristic lengthscales in flat band superconductors
• Quantum spin spiral ground state of the ferrimagnetic sawtooth chain
• Critical States Generators from Perturbed Flatbands
• Thermodynamics of the $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet
• Non-ergodic one-magnon magnetization dynamics of the antiferromagnetic delta chain
• Crystal growth, characterization and phase transition of PbCuTe${}_2$O${}_6$
• Flat-band quantum communication induced by disorder
• One-dimensional flat bands and Dirac cones in narrow zigzag dice lattice ribbons
• Ferromagnetism in armchair graphene nanoribbon heterostructures
• Flat bands and magnetism in $\mathbf{F}{\mathbf{e}}_4\mathbf{GeT}{\mathbf{e}}_2$ and $\mathbf{F}{\mathbf{e}}_5\mathbf{GeT}{\mathbf{e}}_2$ due to bipartite crystal lattices
• Atacamite Cu${}_2$Cl(OH)${}_3$ in High Magnetic Fields: Quantum Criticality and Dimensional Reduction of a Sawtooth-Chain Compound
• Magneto- and barocaloric properties of the ferro-antiferromagnetic sawtooth chain
• Interplay of many-body interactions and quasiperiodic disorder in the all-band-flat diamond chain
• A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system
• Permanent oscillations and solitary wave behavior in flatband Heisenberg quantum spin systems
• Trapping Hard-Core Bosons in Flatband Lattices
• Two-dimensional spin models with macroscopic degeneracy
• Macroscopic ground state degeneracy of the ferro-antiferromagnetic Heisenberg model on diamond-decorated lattices
• Frustrated kagome-lattice bilayer quantum Heisenberg antiferromagnet
• Zero-energy excitation in the classical kagome antiferromagnet NaBa${}_2$Mn${}_3$F${}_{11}$
• Ground state spin and excitation energies in half-filled Lieb lattices
• Six magnetization plateau phases in a spin-1/2 distorted kagome antiferromagnet: application to ${\mathrm{Y}}_3{\mathrm{Cu}}_9(\mathrm{OH}{)}_{19}{\mathrm{Cl}}_8$
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Mode conversion and resonant absorption in inhomogeneous materials with flat bands
• Information Dynamics in a Model with Hilbert Space Fragmentation
• Finite temperatures and flat bands: the Hubbard model on three-dimensional Lieb lattices
• Identifying Instabilities with Quantum Geometry in Flat Band Systems
• Macroscopic degeneracy of ground state in the frustrated Heisenberg diamond chain
• Anomalous Diffusion, Prethermalization, and Particle Binding in an Interacting Flat Band System
• Quantum engineering for compactly localized states in disordered Lieb lattices
• Magnetic properties of delta- and kagome-like chains with competing interactions
• Re-entrant topological order in strongly correlated nanowire due to Rashba spin-orbit coupling
• Selective band interaction and long-range hopping in a structured environment with giant atoms
• Symmetry-protected flatband condition for Hamiltonians with local symmetry
• Spin triangle chain with ferromagnetic and antiferromagnetic interactions on the transition line
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• In-band supratransmission in nonlinear flat band lattices
• One-dimensional Dexter-type excitonic topological phase transition
• Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry
• Resonant cavity-QED with chiral flat bands
• Nonlinear compact localized modes in flux-dressed octagonal-diamond photonic lattice
• The magnetization process of classical Heisenberg magnets with non-coplanar cuboc ground states
• Topological phase transition and its stability against an applied magnetic field in a class of low dimensional decorated lattices
• Magnetization plateaus, spin-canted orders and field-induced transitions in a spin-1/2 Heisenberg antiferromagnet on a distorted diamond-decorated honeycomb lattice
• Localization and Flat Bands in Bond-Inflated Lattices
• Phase diagram and macroscopic ground state degeneracy of frustrated spin-1/2 anisotropic Heisenberg model on diamond-decorated lattices
• Influence of flat bands on RKKY interaction: perspective of Fano defects
• Heat percolation in many-body flatband localizing systems
• Magnetic properties of ferro-antiferromagnetic spin triangle chain
• Flat band mediated photon-photon interactions in 2D waveguide QED networks
• Non-ergodic one-magnon magnetization dynamics of the kagome lattice antiferromagnet
• Flat bands and band touching from real-space topology in hyperbolic lattices
• Towards lattice-gas description of low-temperature properties above the Haldane and cluster-based Haldane ground states of a mixed spin-(1,1/2) Heisenberg octahedral chain
• On flat bands in the $J_1$-$J_2$-$J_3$ XXZ sawtooth chain
• Compact localized currents in flat bands with broken time-reversal symmetry
• Quantum Heisenberg antiferromagnet in a field on the Tasaki square lattice
• Unveiling the degeneracy of bound magnon crystals from magnetic and thermodynamic features of the spin-1/2 Heisenberg octahedral chain
• Electric-field driven flat bands in the distorted sawtooth chain via the Katsura-Nagaosa-Balatsky mechanism
• Using near-flat-band electrons for read-out of molecular spin qubit entangled states