Virtual Topological Insulators with Real Quantized Physics

Abstract

A concrete strategy is presented for generating strong topological insulators in $d+d^{\prime }$ dimensions which have quantized physics in $d$ dimensions. Here, $d$ counts the physical and $d^{\prime }$ the virtual dimensions. It consists of seeking $d$-dimensional representations of operator algebras which are usually defined in $d+d^{\prime }$ dimensions where topological elements display strong topological invariants. The invariants are shown, however, to be fully determined by the physical dimensions, in the sense that their measurement can be done at fixed virtual coordinates. We solve the bulk-boundary correspondence and show that the boundary invariants are also fully determined by the physical coordinates. We analyze the virtual Chern insulator in $(1+1)$-dimensions realized in Ref.~\cite{KrausPRL2012hh} and predict quantized forces at the edges. We generate a novel topological system in $(3+1)$-dimensions, which is predicted to have quantized magneto-electric response.

Proof that the invariants can be computed at fixed virtual coordinate is included

References in corpus (6)

• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Measurement of a topological edge invariant in a microwave network
• A Non-Commutative Formula for the Isotropic Magneto-Electric Response