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Abstract
The superfluid weight of a generic lattice model with attractive Hubbard interaction is computed analytically in the isolated band limit within the generalized random phase approximation. Timereversal symmetry, spin rotational symmetry, and the uniform pairing condition are assumed. It is found that the relation obtained in [https://link.aps.org/doi/10.1103/PhysRevB.106.014518] between the superfluid weight in the flat band limit and the socalled minimal quantum metric is valid even at the level of the generalized random phase approximation. For an isolated, but not necessarily flat, band it is found that the correction to the superfluid weight obtained from the generalized random phase approximation $D_{\rm s}^{(1)} = D_{\rm s,c}^{(1)}+D_{\rm s,g}^{(1)}$ is also the sum of a conventional contribution $D_{\rm s,c}^{(1)}$ and a geometric contribution $D_{\rm s,g}^{(1)}$, as in the case of the known meanfield result $D_{\rm s}^{(0)}=D_{\rm s,c}^{(0)}+D_{\rm s,g}^{(0)}$, in which the geometric term $D_{\rm s,g}^{(0)}$ is a weighted average of the quantum metric. The conventional contribution is geometry independent, that is independent of the orbital positions, while it is possible to find a preferred, or natural, set of orbital positions such that $D_{\rm s,g}^{(1)}=0$. Useful analytic expressions are derived for both the natural orbital positions and the minimal quantum metric, including its extension to bands that are not necessarily flat. Finally, using some simple examples, it is argued that the natural orbital positions may lead to a more refined classification of the topological properties of the band structure.
Original language  English 

Journal  arXiv.org 
Publication status  Accepted/In press  21 Aug 2023 
MoE publication type  B1 Nonrefereed journal articles 
Keywords
 Condensed Matter  Superconductivity
 Condensed Matter  Strongly Correlated Electrons
 Quantum Physics
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: Superfluidity, topology and disorder in lattice models with flat bands  SUPERFLAT
Peotta, S., Swaminathan, K. & Müftüoglu, M.
01/09/2023 → 31/08/2025
Project: Academy of Finland: Other research funding

: Peotta Sebastiano ATkulut
Peotta, S., Swaminathan, K., Tadros, P. & Müftüoglu, M.
01/09/2020 → 31/08/2023
Project: Academy of Finland: Other research funding