"Quantum Geometric Nesting" and Solvable Model Flat-Band Systems

Abstract

We introduce the concept of "quantum geometric nesting'' (QGN) to characterize the idealized ordering tendencies of certain flat-band systems implicit in the geometric structure of the flat-band subspace. Perfect QGN implies the existence of an infinite class of local interactions that can be explicitly constructed and give rise to solvable ground states with various forms of possible fermion bi-linear order, including flavor ferromagnetism, density waves, and superconductivity. For the ideal Hamiltonians constructed in this way, we show that certain aspects of the low-energy spectrum can also be exactly computed including, in the superconducting case, the phase stiffness. Examples of perfect QGN include flat bands with certain symmetries (e.g. chiral or time-reversal), and non-symmetry-related cases exemplified with an engineered model for pair-density-wave. Extending this approach, we obtain exact superconducting ground states with nontrivial pairing symmetry.

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• Enhanced pair-density-wave vertices in a bilayer Hubbard model at half-filling
• Superfluid stiffness bounds in time-reversal symmetric superconductors
• Identifying Instabilities with Quantum Geometry in Flat Band Systems
• Models of interacting bosons with exact ground states: a unified approach
• Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity
• Quantum geometry in correlated electron phases: from flat band to dispersive band
• Quantum Geometric Helical Superconductivity
• Certain BCS wavefunctions are quantum many-body scars
• Unconventional superconducting correlations in fermionic many-body scars
• Three-dimensional flat bands and possible interlayer triplet pairing superconductivity in the alternating twisted NbSe${}_2$ moiré bulk
• Bootstrapping Flat-band Superconductors: Rigorous Lower Bounds on Superfluid Stiffness
• Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
• Gaplessness from disorder and quantum geometry in gapped superconductors
• Quantum geometric magnetic monopole and two-phase superconductivity in CeRh${}_2$As${}_2$