arXiv subjects

Nicolas Levasseur

Publications and source records attributed to Nicolas Levasseur.

3 recordsLinked to original sources

arXiv2026

Topological Boundary States and the Edge Chain in Semi-Infinite Two-Dimensional Insulators

We show that it is possible to compute the adiabatically protected edge and corner states of semi-infinite, two-dimensional, topological insulators by considering the first layer of lattice sites, what we call the "edge chain," independently from the bulk. We start by accepting this claim as an ansatz, then, using the Shemesh theorem, we show that the edge states one finds using our procedure are adiabatically protected, provided we restrict ourselves to adiabatic evolutions that do not break chiral symmetry. We show explicit examples of our method in a 2D extension of the SSH model, the SSH3 model, the Haldane model and the Breathing Kagome Lattice.

cond-mat.mes-hall↗

arXiv2026

Bulk-Boundary Correspondence in Semi-Infinite Chains from Sublattice Zeros

We provide an alternative derivation of the bulk-boundary correspondence for semi-infinite chains. To describe edge states, we analytically continue the usual Bloch Hamiltonian to complex wave vectors $k$. To start, we note that the zeros of a Bloch wavefunction are related to edge states, at least in systems with nearest-neighbour hoppings. We show that an analytically continued Bloch Hamiltonian with chiral symmetry has exceptional points, where two different states coalesce. These special points are related to the adiabatic protection of edge states. We derive a winding number that counts the number of topological edge states protected by chiral symmetry.

cond-mat.mes-hall↗

arXiv2026

The typicality of symmetry-induced entanglement

In the presence of a globally conserved charge $N$, a natural question is whether a given separable state can be separated into charge-conserving components. We dub this problem the Symmetric Separability Problem (SSP). On random states, the SSP is answered negatively with probability one for almost all $N$. Using a witness to the failure of symmetric separability, namely the number entanglement (NE) introduced in arXiv:2110.09388, we show that most symmetric and separable states are actually far from being symmetrically separable, with the NE featuring Gaussian concentration around a strictly positive mean value. We discuss some consequences of our results for quantum tasks in the presence of a superselection rule or in the absence of a common reference frame. Progress is made on the question of the size of the separable space constrained by $N$. We also touch upon the question of the complexity of SSP, and multiparty entanglement.

quant-ph↗