Full counting statistics in the many-body Hatano-Nelson model

TL;DR

This paper investigates the effects of non-Hermitian physics in the interacting Hatano-Nelson model, revealing how many-body interactions modify localization, density profiles, and probability distributions, with implications for both fermionic and bosonic systems.

Contribution

It provides the first detailed analysis of full counting statistics and many-body effects in the non-Hermitian Hatano-Nelson model with interactions and open boundaries.

Findings

Density profile becomes only slightly tilted in the interacting system.

Friedel oscillations show a beating pattern due to Fermi wavenumber modification.

Particle distribution over finite intervals follows a normal distribution with mean scaling with the imaginary vector potential.

Abstract

We study non-hermitian many-body physics in the interacting Hatano-Nelson model with open boundary condition. The violation of reciprocity, resulting from an imaginary vector potential, induces the non-hermitian skin-effect and causes exponential localization for all single particle eigenfunctions in the non-interacting limit. Nevertheless, the density profile of the interacting system becomes only slightly tilted relative to the average filling. The Friedel oscillations exhibit a beating pattern due to the modification of the Fermi wavenumber. The probability distribution of particles over any finite interval is the normal distribution, whose mean scales with the imaginary vector potential and the variance is symmetric to the center of the chain. This is confirmed by several numerically exact methods even for relatively small systems. These features are expected to be generic not only for fermions, which naturally repel each other due to Pauli's exclusion principle, but for interacting bosons as well. Our findings indicate that many-body effects can significantly alter and conceal the single particle properties and the skin effect in non-hermitian systems.