Bipartite fluctuations and charge fractionalization in quantum wires

We introduce a quantum information method for measuring fractional charges in ballistic quantum wires generalizing bipartite fluctuations to the chiral quasiparticles in Luttinger liquids, i.e., analyzing and summing charge and current fluctuations in a region of the wire. Bipartite fluctuations at equilibrium are characterized through a logarithmic scaling with distance encoding the entangled nature of these fractional charges in onedimensional (1D) fluids. This approach clarifies the physical meaning of the dephasing factor of electronic interferences in a ballistic ring geometry at zero temperature, as a result of charge fractionalization. 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 (DMRG). Adding a potential difference between the two sides (parties) of the wire, bipartite fluctuations can detect a bound state localized at the interface through the Jackiw-Rebbi model coexisting with fractional charges.