Effects of the Hubbard interaction on the quantum metric
arXiv:2412.02753 · doi:10.1103/PhysRevB.111.085143
Abstract
Quantum geometry provides important information about the structure and topology of quantum states in various forms of quantum matter. The information contained therein has profound effects on observable quantities such as superconducting weight, Drude weight, and optical responses. Motivated by the recent advances in flat-band interacting systems, we investigate the role of interaction effects on the quantum metric. By using the fermionic Creutz ladder as a representative system, we show that the repulsive Hubbard interaction monotonically suppresses the quantum metric. While the eigenstates and their overlap quantifying the quantum metric can be obtained exactly in the presence of interactions through exact diagonalization, this method is limited to small system sizes. Alternatively, two theoretical proposals, the generalized quantum metric and the dressed quantum metric, suggest using renormalized Green's functions to define the interacting quantum metric. By comparing these analytical approaches with results from exact diagonalization, we show that the dressed quantum metric provides a better fit to the exact diagonalization results. Our conclusion holds for both flat-band and dispersive systems.
arXiv comment15 pages, 9 figures; close to the published version
References in corpus (45)
- Topological Insulators
- Maximally-localized generalized Wannier functions for composite energy bands
- Anomalous Hall effect
- Weyl and Dirac Semimetals in Three Dimensional Solids
- Maximally localized Wannier functions: Theory and applications
- Graphene Bilayers with a Twist
- Interfacial mode coupling as the origin of the enhancement of Tc in FeSe films on SrTiO3
- Superfluidity in topologically nontrivial flat bands
- Fidelity approach to quantum phase transitions
- Fidelity, dynamic structure factor, and susceptibility in critical phenomena
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
- Polarization and localization in insulators: generating function approach
- Superfluidity and Quantum Geometry in Twisted Multilayer Systems
- QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
- Topological quantum matter with cold atoms
- Band geometry of fractional topological insulators
- Band geometry, Berry curvature and superfluid weight
- Direct measurement of the quantum geometric tensor in a two-dimensional continuous medium
- Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals
- End states, ladder compounds, and domain wall fermions
- Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
- Exploring Interacting Topological Insulators with Ultracold Atoms: the Synthetic Creutz-Hubbard Model
- Effective theory and emergent symmetry in the flat bands of attractive Hubbard models
- An Optical-Lattice-Based Quantum Simulator For Relativistic Field Theories and Topological Insulators
- Topological and geometrical aspects of band theory
- Enhanced superconductivity due to forward scattering in FeSe thin films on SrTiO3 substrates
- Experimental measurement of the quantum geometric tensor using coupled qubits in diamond
- Universal Substrate Effect on the Superconductivity of FeSe Monolayer Films
- Geometric stability of topological lattice phases
- Elementary excitations in the -chain
- On Quantum Solitons in the Sawtooth Lattice
- Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole
- Topological Creutz Ladder in a Resonantly Shaken 1D Optical Lattice
- Strong Inter-valley Electron-Phonon Coupling in Magic-Angle Twisted Bilayer Graphene
- Measurements of the quantum geometric tensor in solids
- Probing localization and quantum geometry by spectroscopy
- Multiband full-bandwidth anisotropic Eliashberg theory of interfacial electron-phonon coupling and high-T superconductivity in FeSe/SrTiO
- Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker
- Quantum plasmonic non-reciprocity in parity-violating magnets
- Stability of fractional Chern insulators with a non-Landau level continuum limit
- Magnetic susceptibility of topological semimetals
- Quantum metric on the Brillouin Zone in correlated electron systems and its relation to topology for Chern insulators
- Drude weight and the many-body quantum metric in one-dimensional Bose systems
- Detecting the spread of valence band Wannier functions by optical sum rules
- Cascade of replica bands in flat band systems: predictions for twisted bilayer graphene