11 citations · 21 across the 3 of their papers we have counts for
6 papers
Absence of localization in two-dimensional Clifford circuits
Tom Farshi, Jonas Richter, Daniele Toniolo +2
We analyze a Floquet circuit with random Clifford gates in one and two spatial dimensions. By using random graphs and methods from percolation theory, we prove in the two dimension…
The Bott index of two unitary operators and the integer quantum Hall effect
Daniele Toniolo
The Bott index of two unitary operators on an infinite dimensional Hilbert space is defined. homotopic invariance with respect to multiplicative unitary perturbations of the type i…
Mixing and localisation in random time-periodic quantum circuits of Clifford unitaries
Tom Farshi, Daniele Toniolo, Carlos E. González-Guillén +2
How much does local and time-periodic dynamics resemble a random unitary? In the present work we address this question by using the Clifford formalism from quantum computation. We…
Dimensional reduction and scattering formulation for even topological invariants
Hermann Schulz-Baldes, Daniele Toniolo
Strong invariants of even-dimensional topological insulators of independent Fermions are expressed in terms of an invertible operator on the Hilbert space over the boundary. It is…
Time-dependent topological systems: A study of the Bott index
Daniele Toniolo
The Bott index is an index that discerns among pairs of unitary matrices that can or cannot be approximated by a pair of commuting unitary matrices. It has been successfully employ…
On the Bott index of unitary matrices on a finite torus
Daniele Toniolo
This article reviews the foundations of the theory of the Bott index of a pair of unitary matrices in the context of condensed matter theory, as developed by Hastings and Loring in…