Subproduct systems arising from Temperley–Lieb combinatorics provide a rich class of quantum structures that interpolate between algebraic and topological features of noncommutative spaces. These systems naturally generate Cuntz–Pimsner algebras, which can be viewed as noncommutative analogues of function algebras on quantum homogeneous spaces or algebraic subsets of noncommutative...
We define a many-body topological index to classify invertible and U(1)-symmetric states over the CAR algebra of interacting electrons on an infinitely extended two-dimensional lattice. The definition relies on a magnetic flux insertion through the origin in a quasi-adiabatic way and on the properties of short range entangled states. The index is integer-valued and invariant under...
Monopoles can be induced by band crossing points that generate a gauge-invariant vector field, the Berry curvature, whose flux is quantized. For instance, in 3D space, this flux corresponds to the first Chern number. In turn, the value of this topological invariant gives the number of unidirectional modes, or spectral flow, of the system. In this talk, I would like to show that certain...
This talk is about the asymptotic spectral theory of tridiagonal Toeplitz matrices with matrix entries, with periodicity broken on a finite number of entries. Varying the ranks of these perturbations allow to interpolate between open boundary and circulant Toeplitz matrices. While the continuous parts of the limit spectrum only depends in a crucial manner on these ranks and no other aspect...
