Entanglement spectrum of a topological phase in one dimension

Entanglement of topological phase factors

The topological phase factor induced on interfering electrons by external quantum electromagnetic fields has been studied. Two and three electron interference experiments inside distant cavities are considered and the influence of correlated photons on the phase factors is investigated. It is shown that the classical or quantum correlations of the irradiating photons are transferred to the topo...

Entanglement spectrum of topological insulators and superconductors.

We study two a priori unrelated constructions: the spectrum of edge modes in a band topological insulator or superconductor with a physical edge, and the ground state entanglement spectrum in an extended system where an edge is simulated by an entanglement bipartition. We prove an exact relation between the ground state entanglement spectrum of such a system and the spectrum edge modes of the c...

Topological phases of fermions in one dimension

In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of one-dimensional systems. We focus on the time-reversal-invariant Majorana chain (BDI symmetry class). While the band classification yields an integer topological index k, it is known that phases characterized by values of k in the same equivalence class...

Topological superconducting phases in one dimension

Periodicity of the Spectrum in Dimension One

A bounded measurable set Ω, of Lebesgue measure 1, in the real line is called spectral if there is a set Λ of real numbers (“frequencies”) such that the exponential functions eλ(x) = exp(2πiλx), λ ∈ Λ, form a complete orthonormal system of L2(Ω). Such a set Λ is called a spectrum of Ω. In this note we prove that any spectrum Λ of a bounded measurable set Ω ⊆ R must be periodic.