A groupoid approach to interacting fermions

Abstract

We consider the algebra $\dot{\Sigma }(\mathcal{L})$ generated by the inner-limit derivations over the $\mathrm{GICAR}$ algebra of a fermion gas populating an aperiodic Delone set $\mathcal{L}$. Under standard physical assumptions such as finite interaction range, Galilean invariance and continuity with respect to the aperiodic lattice, we demonstrate that the image of $\dot{\Sigma }(\mathcal{L})$ through the Fock representation can be completed to a groupoid-solvable pro-$C^{\ast }$-algebra. Our result is the first step towards unlocking the $K$-theoretic tools available for separable $C^{\ast }$-algebra for applications in the context of interacting fermions.

References in corpus (3)

• Revealing the boundary Weyl physics of the four-dimensional Hall effect via phason engineering in metamaterials
• Topological Lattice Defects by Groupoid Methods and Kasparov's KK-Theory
• Physical rendering of synthetic spaces for topological sound transport

Cited by in corpus (4)

• C*-framework for higher-order bulk-boundary correspondences
• Classifying the Dynamics of Architected Materials by Groupoid Methods
• Robustness of topological phases on aperiodic lattices
• Cyclic cocycles and quantized pairings in materials science