Many-Body Quantum Geometric Dipole
arXiv:2406.12089 · doi:10.1103/PhysRevB.111.035158
Abstract
Collective excitations of many-body electron systems can carry internal structure, tied to the quantum geometry of the Hilbert space in which they are embedded. This has been shown explicitly for particle-hole-like excitations, which carry a ``quantum geometric dipole'' (QGD) that is essentially an electric dipole moment associated with the state. We demonstrate in this work that this property can be formulated in a generic way, which does not require wavefunctions expressed in terms of single particle-hole states. Our formulation exploits the density matrix associated with a branch of excitations that evolves continuously with its momentum , from which one may extract single-particle states allowing a construction of the QGD. We demonstrate the formulation using the single-mode approximation for excited states of two quantum Hall systems: the first for an integrally filled Landau level, and the second for a fractional quantum Hall state at filling factor , with an odd integer. In both cases we obtain the same result for the QGD, which can be attributed to the translational invariance assumed of the system. Our study demonstrates that the QGD is an intrinsic property of collective modes which is valid beyond approximations one might make for their wavefunctions.
19 pages, 4 figures
References in corpus (43)
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Topological Order and the Quantum Spin Hall Effect
- Berry Phase Effects on Electronic Properties
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- Anomalous Hall effect
- Moire bands in twisted double-layer graphene
- The quantum spin Hall effect and topological insulators
- Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
- Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
- Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
- Superfluidity in topologically nontrivial flat bands
- Geometric origin of superfluidity in the Lieb lattice flat band
- Superfluidity and Quantum Geometry in Twisted Multilayer Systems
- Band geometry, Berry curvature and superfluid weight
- Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene
- Essay: Where Can Quantum Geometry Lead Us?
- Berry phase modification to the energy spectrum of excitons
- Superfluid weight bounds from symmetry and quantum geometry in flat bands
- Chiral plasmons without magnetic field
- Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations
- Collective modes of doped graphene and a standard 2DEG in a strong magnetic field: linear magneto-plasmons versus magneto-excitons
- Semi-classical wave packet dynamics in non-uniform electric fields
- Berry Phase Effect on Exciton Transport and Bose Einstein Condensate
- Optical Spectral Weight, Phase Stiffness and Tc Bounds for Trivial and Topological Flat Band Superconductors
- Orbital Magneto-Nonlinear Anomalous Hall Effect in Kagome Magnet FeSn
- Exciton band topology in spontaneous quantum anomalous Hall insulators: applications to twisted bilayer graphene
- The magnetic field particle-hole excitation spectrum in doped graphene and in a standard two-dimensional electron gas
- Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
- The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
- Quantum metric contribution to the pair mass in spin-orbit coupled Fermi superfluids
- Diamagnetic response and phase stiffness for interacting isolated narrow bands
- Interacting topological quantum chemistry of Mott atomic limits
- Theory of topological exciton insulators and condensates in flat Chern bands
- Superconductivity-induced spectral weight transfer due to quantum geometry
- Quantum plasmonic non-reciprocity in parity-violating magnets
- Geometric Stiffness in Interlayer Exciton Condensates
- Anomalous exciton transport in response to a uniform, in-plane electric field
- Quantum Geometric Exciton Drift Velocity
- Magnetoexcitons in quantum-ring structures: a novel magnetic interference effect
- Role of the Berry curvature on BCS-type superconductivity in two-dimensional materials
- Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors
- Plasmonic Transverse Dipole Moment in Chiral Fermion Nanowires