Bipartite Fluctuations and Charge Fractionalization in Quantum Wires

Abstract: We introduce a quantum information method for measuring fractional charges in ballistic quantum wires generalizing bipartite fluctuations to the chiral quasiparticles in Luttinger liquids. This is equivalent to add charge and current fluctuations in a region of the wire. This reveals from an equilibrium approach the entangled nature of the two counter-propagating fractional charges associated to the same electron in the system. Bipartite fluctuations at equilibrium are characterized through a logarithmic scaling with distance encoding the entangled nature of these fractional charges in one-dimensional (1D) fluids. This approach also clarifies the physical meaning of the dephasing factor of electronic interferences in a ring geometry at zero temperature from a space-time correspondence in 1D. We formulate an analogy towards ground-state energetics. We show how bipartite current fluctuations represent a useful tool to locate quantum phase transitions associated to Mott physics. We address a spin chain equivalence and verify the fractional charges through an algorithm such as Density Matrix Renormalization Group. Adding a potential difference between the two sides (parties) of the wire, also we show how bipartite fluctuations can detect the presence of a bound state localized at the interface through the Jackiw-Rebbi model coexisting with fractional charges.