Non-Bloch self-energy of dissipative interacting fermions

TL;DR

This paper develops a diagrammatic approach to analyze the non-Hermitian skin effect in dissipative interacting fermions, revealing how interactions modify quasiparticle states and the system's spectrum.

Contribution

It introduces a perturbative framework for calculating self-energy and quasiparticle properties in dissipative fermionic systems exhibiting non-Hermitian skin effect.

Findings

Derived an exact integral representation for self-energy corrections.

Confirmed the theory's predictions with high-precision numerical calculations.

Identified interaction-induced renormalization of the generalized Brillouin zone.

Abstract

The non-Hermitian skin effect describes the phenomenon of exponential localization of single-particle eigenstates near the boundary of the system. We consider its generalization to the many-body regime by investigating a general class of interacting fermion lattice models in Markovian open quantum systems. Therein, the elementary excitations from the "vacuum" (steady state) are given by two types of dissipative fermionic modes composed of single-fermion operators, which govern the long-time nonequilibrium dynamics. We perturbatively calculate the self-energy matrix of these bare modes in the presence of interactions, and utilize the non-Bloch band theory to derive an exact integral representation. By imposing complex momentum conservation, we obtain a simplified expression for corrections to Liouvillian spectrum that agrees well with numerical calculations to high precision. We further perform perturbative analysis of Liouvillian eigenstates and identify signatures of interaction-enhanced NHSE at the quasiparticle level, manifested as renormalization of the generalized Brillouin zone. Our results establish a diagrammatic framework for dissipative interacting fermions with non-Hermitian skin effect in a description of full-fledged Lindblad master equations, which resembles Fermi liquid theory in terms of interaction-dressed quasiparticles.