Locality of the windowed local density of states

TL;DR

This paper introduces the windowed local density of states (wLDOS), a generalized, local, and computable version of LDOS for infinite systems, with applications demonstrated on a Fibonacci SSH model.

Contribution

It defines the wLDOS, proves its locality and computability for infinite systems, and applies it to analyze topological edge states in a non-periodic model.

Findings

wLDOS is local and can be computed with spatial truncations

wLDOS is well-defined for infinite systems under natural conditions

Numerical results show edge and bulk properties in the Fibonacci SSH model

Abstract

We introduce a generalization of local density of states which is "windowed" with respect to position and energy, called the windowed local density of states (wLDOS). This definition generalizes the usual LDOS in the sense that the usual LDOS is recovered in the limit where the position window captures individual sites and the energy window is a delta distribution. We prove that the wLDOS is local in the sense that it can be computed up to arbitrarily small error using spatial truncations of the system Hamiltonian. Using this result we prove that the wLDOS is well-defined and computable for infinite systems satisfying some natural assumptions. We finally present numerical computations of the wLDOS at the edge and in the bulk of a "Fibonacci SSH model", a one-dimensional non-periodic model with topological edge states.