TY - JOUR
T1 - Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
AU - Han, Zhaoyu
AU - Herzog-Arbeitman, Jonah
AU - Bernevig, B. Andrei
AU - Kivelson, Steven A.
N1 - Publisher Copyright:
© 2024 authors.
PY - 2024/10
Y1 - 2024/10
N2 - 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 bilinear 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.
AB - 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 bilinear 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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U2 - 10.1103/PhysRevX.14.041004
DO - 10.1103/PhysRevX.14.041004
M3 - Article
AN - SCOPUS:85206310009
SN - 2160-3308
VL - 14
JO - Physical Review X
JF - Physical Review X
IS - 4
M1 - 041004
ER -