Bipartite Fluctuations and Charge Fractionalization in Quantum Wires

TL;DR

This paper introduces a quantum information approach using bipartite fluctuations to measure and analyze fractional charges and quantum phase transitions in one-dimensional quantum wires and related systems.

Contribution

It generalizes bipartite fluctuation analysis to chiral quasiparticles in Luttinger liquids, linking charge fractionalization to entanglement and quantum phase transitions.

Findings

Bipartite fluctuations scale logarithmically with distance, revealing fractional charges.

The method clarifies the dephasing factor in electronic interference at zero temperature.

Bipartite current fluctuations can identify quantum phase transitions and localized bound states.

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, 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 one-dimensional (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.