Exploring excited eigenstates of many-body systems using the functional renormalization group

TL;DR

This paper develops functional renormalization group methods to compute correlation functions in excited states of large many-body fermionic systems, providing new tools for analyzing non-ground state properties.

Contribution

It introduces approximate RG schemes for excited eigenstates and benchmarks them on a 1D fermionic chain, exploring their effectiveness and limitations.

Findings

Power-law behaviors persist in lowly-excited states.

Spectral functions of high-energy excitations show multiple Fermi edges.

The methods are validated against known results in Luttinger liquids.

Abstract

We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thouroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two `toy applications' from the world of Luttinger liquid physics: the survival of power laws in lowly-excited states as well as the spectral function of high-energy `block' excitations which feature several single-particle Fermi edges.