Two-body problem in a multiband lattice and the role of quantum geometry

Abstract

We consider the two-body problem in a periodic potential, and study the bound-state dispersion of a spin-$\uparrow$ fermion that is interacting with a spin-$\downarrow$ fermion through a short-range attractive interaction. Based on a variational approach, we obtain the exact solution of the dispersion in the form of a set of self-consistency equations, and apply it to tight-binding Hamiltonians with onsite interactions. We pay special attention to the bipartite lattices with a two-point basis that exhibit time-reversal symmetry, and show that the lowest-energy bound states disperse quadratically with momentum, whose effective-mass tensor is partially controlled by the quantum metric tensor of the underlying Bloch states. In particular, we apply our theory to the Mielke checkerboard lattice, and study the special role played by the interband processes in producing a finite effective mass for the bound states in a non-isolated flat band.

6 pages with 2 figures; to appear in PRA

References in corpus (6)

• Band geometry, Berry curvature and superfluid weight
• Exotic electronic states in the world of flat bands: from theory to material
• Two-particle states in the Hubbard model
• Observation of flat band for terahertz spoof plasmon in metallic kagomé lattice
• Origin of flat-band superfluidity on the Mielke checkerboard lattice
• Tunneling properties of a bound pair of Fermi atoms in an optical lattice

Cited by in corpus (25)

• Superfluidity and Quantum Geometry in Twisted Multilayer Systems
• Superfluid weight bounds from symmetry and quantum geometry in flat bands
• Extracting quantum-geometric effects from Ginzburg-Landau theory in a multiband Hubbard model
• Geometric Stiffness in Interlayer Exciton Condensates
• Suppression of non-equilibrium quasiparticle transport in flat band superconductors
• Effective-mass tensor of the two-body bound states and the quantum-metric tensor of the underlying Bloch states
• Quantum Metric in Step Response
• Quantum-geometric perspective on spin-orbit-coupled Bose superfluids
• Pairs, trimers and BCS-BEC crossover near a flat band: the sawtooth lattice
• Polaron spectra and edge singularities for correlated flat bands
• Quantum-geometric contribution to the Bogoliubov modes in a two-band Bose-Einstein condensate
• Three-body problem in a multiband Hubbard model
• Topological two-body bands in a multiband Hubbard model
• Pair size and quantum geometry in a multiband Hubbard model
• Superconductivity and pair density waves from nearest-neighbor interactions in frustrated lattice geometries
• Electron Interactions in Rashba Materials
• Electron pairs bound by the spin-orbit interaction in 2D gated Rashba materials with two-band spectrum
• Dimers, trimers, tetramers, and other multimers in a multiband Bose-Hubbard model
• Stability of $(N+1)$-body fermion clusters in multiband Hubbard model
• Chern numbers for the two-body Hofstadter-Hubbard butterfly
• Superfluid stiffness of superconductors with delicate topology
• Revisiting flat band superconductivity: dependence on minimal quantum metric and band touchings
• Variational approach for the two-body problem in a multiband extended-Hubbard model
• Topological two-body interaction obstructing trivial ground states: an indicator of fractional Chern insulators
• Correlation lengths of flat-band superconductivity from quantum geometry