Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
arXiv:2410.16352 · doi:10.1103/xmz7-jgl6
Abstract
Inspired by the discovery of a variety of correlated insulators in the moiré universe, controlled by interactions projected to a set of isolated bands with a narrow bandwidth, we examine here a partial sum-rule associated with the inverse frequency-weighted optical conductivity restricted to low-energies. Unlike standard sum-rules that extend out to frequencies, which include contributions from inter-band transitions, we focus here on transitions associated with the degrees of freedom. We analyze the partial sum-rule in a non-perturbative but "solvable" limit for a variety of correlation-induced insulators. This includes (i) magic-angle twisted bilayer graphene at integer-filling with projected Coulomb interactions, starting from the chiral flat-band limit and including realistic perturbations, (ii) fractional fillings of Chern-bands which support generalized Laughlin-like states, starting from a Landau-level and including a periodic potential and magnetic-field, respectively, drawing connections to twisted MoTe, and (iii) integer filling in toy-models of non-topological flat-bands with a tunable quantum geometry in the presence of repulsive interactions. The partial sum-rule in all of these examples is implicitly constrained by the form of the band quantum geometry via the low-lying excitation spectrum, but is not related to it explicitly. For interacting Slater-determinant insulators, the partial sum-rule is related to a new quantity -- "many-body projected quantum geometry" -- obtained from the interaction-renormalized electronic bands. We also point out an intriguing connection between the partial sum-rule and the quantum Fisher information associated with the projected many-body position operator.
Main text: 16 pages, 5 figures, Supplementary information: 5 pages
References in corpus (108)
- Topological Insulators
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- Moire bands in twisted double-layer graphene
- Tuning superconductivity in twisted bilayer graphene
- Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
- Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
- Intrinsic quantized anomalous Hall effect in a moiré heterostructure
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Quantum Spin Liquids
- Magic Angle Spectroscopy
- Origin of Magic Angles in Twisted Bilayer Graphene
- Topological insulators in twisted transition metal dichalcogenide homobilayers
- Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
- Imaging Electronic Correlations in Twisted Bilayer Graphene near the Magic Angle
- Charge-Order and Broken Rotational Symmetry in Magic Angle Twisted Bilayer Graphene
- Fractional quantum Hall effect in the absence of Landau levels
- Spectroscopic signatures of many-body correlations in magic angle twisted bilayer graphene
- Fractional Chern Insulator
- Fisher information and multiparticle entanglement
- Multipartite entanglement and high precision metrology
- Fractional Chern insulators in magic-angle twisted bilayer graphene
- Integer and fractional Chern insulators in twisted bilayer MoTe2
- Untying the insulating and superconducting orders in magic-angle graphene
- Fractional Quantum Hall Physics in Topological Flat Bands
- Cascade of electronic transitions in magic-angle twisted bilayer graphene
- Strongly Correlated Chern Insulators in Magic-Angle Twisted Bilayer Graphene
- Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene
- Decoupling superconductivity and correlated insulators in twisted bilayer graphene
- Fisher Information and entanglement of non-Gaussian spin states
- Mapping the twist angle and unconventional Landau levels in magic angle graphene
- Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2
- Nematicity and Competing Orders in Superconducting Magic-Angle Graphene
- Chern Insulators and Topological Flat-bands in Magic-angle Twisted Bilayer Graphene
- Superconductivity without insulating states in twisted bilayer graphene stabilized by monolayer WSe
- Measuring multipartite entanglement via dynamic susceptibilities
- Geometrical Description of the Fractional Quantum Hall Effect
- Polarization and localization in insulators: generating function approach
- Superfluidity and Quantum Geometry in Twisted Multilayer Systems
- Continuous Mott transition in semiconductor moiré superlattices
- Band geometry of fractional topological insulators
- Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
- Fractional Chern Insulator States in Twisted Bilayer Graphene: An Analytical Approach
- Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals
- Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening
- Flavour Hund's Coupling, Correlated Chern Gaps, and Diffusivity in Moiré Flat Bands
- Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
- Hofstadter subband ferromagnetism and symmetry broken Chern insulators in twisted bilayer graphene
- Exact Landau Level Description of Geometry and Interaction in a Flatband
- Entropic evidence for a Pomeranchuk effect in magic angle graphene
- Symmetry broken Chern insulators and magic series of Rashba-like Landau level crossings in magic angle bilayer graphene
- Topology and geometry under the nonlinear electromagnetic spotlight
- Essay: Where Can Quantum Geometry Lead Us?
- Spontaneous fractional Chern insulators in transition metal dichalcogenides Moire superlattices
- Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion
- Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
- Quantum textures of the many-body wavefunctions in magic-angle graphene
- Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
- Efficient simulation of moire materials using the density matrix renormalization group
- Imaging Chern mosaic and Berry-curvature magnetism in magic-angle graphene
- Interplay of Fractional Chern Insulator and Charge-Density-Wave Phases in Twisted Bilayer Graphene
- Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs
- Correlated Hofstadter Spectrum and Flavor Phase Diagram in Magic Angle Graphene
- Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
- Fundamental bound on topological gap
- Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
- Anomalous Hall effect at half filling in twisted bilayer graphene
- Superconductivity, charge density wave, and supersolidity in flat bands with tunable quantum metric
- Bound on resistivity in flat-band materials due to the quantum metric
- Light-matter coupling and quantum geometry in moiré materials
- Tunable moiré materials for probing Berry physics and topology
- Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators
- Power-law Conductivity inside the Mott gap: application to
- Ideal Chern bands are Landau levels in curved space
- Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
- Intrinsic anomalous Hall conductivity in a nonuniform electric field
- Fractional Chern insulators with strong interactions far exceeding bandgaps
- Mechanisms for Sub-Gap Optical Conductivity in Herbertsmithite
- Adiabatic Approximation and Aharonov-Casher Bands in Twisted Homobilayer TMDs
- Polarization fluctuations in insulators and metals: New and old theories merge
- Quantized Integrated Shift Effect in Multigap Topological Phases
- Optical manifestations and bounds of topological Euler class
- Generalized -Sum Rules and Kohn formulas on Non-linear Conductivities
- Electron spin resonance and collective excitations in magic-angle twisted bilayer graphene
- Quantum Quench and -Sum Rules on Linear and Non-linear Conductivities
- Neutral Excitations of Quantum Hall States: a Density Matrix Renormalization Group Study
- Topological bound on structure factor
- Variational Mapping of Chern Bands to Landau Levels: Application to Fractional Chern Insulators in Twisted MoTe
- Spin skyrmion gaps as signatures of strong-coupling insulators in magic-angle twisted bilayer graphene
- From entanglement certification with quench dynamics to multipartite entanglement of interacting fermions
- Stability of fractional Chern insulators with a non-Landau level continuum limit
- Upper bounds on superconducting and excitonic phase-stiffness for interacting isolated narrow bands
- Quantum Metric in Step Response
- Quantum entanglement and quantum geometry measured with inelastic X-ray scattering
- Spectral Density and Sum Rules for Second-Order Response Functions
- Low-energy optical sum-rule in moiré graphene
- Topological quantum phase transitions driven by a displacement field in the twisted MoTe2 bilayers
- Optical conductivity of visons in Z2 spin liquids close to a VBS transition on the kagome lattice
- Charge Conservation Beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids
- Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators
- Drude weight of an interacting flat-band metal
- Intraband collective excitations in fractional Chern insulators are dark
- Optical bounds on many-electron localization
- Area-law entanglement from quantum geometry
- Moiré Assisted Fractional Quantum Hall State Spectroscopy
- Compressible quantum liquid with vanishing Drude weight
- A Bound on Topological Gap from Newton's Laws