Renormalization by Continuous Unitary Transformations: One-Dimensional Spinless Fermions

TL;DR

This paper introduces a renormalization method using continuous unitary transformations for one-dimensional spinless fermions, achieving results that align well with exact solutions despite the complexity of fermionic degrees of freedom.

Contribution

It presents a novel renormalization scheme based on continuous unitary transformations that maintains hermiticity and avoids frequency dependence, applied successfully to a 1D fermionic model.

Findings

Results agree well with Bethe ansatz solutions

The method effectively handles fermionic degrees of freedom

Achieves accurate renormalization in one-dimensional systems

Abstract

A renormalization scheme for interacting fermionic systems is presented where the renormalization is carried out in terms of the fermionic degrees of freedom. The scheme is based on continuous unitary transformations of the hamiltonian which stays hermitian throughout the renormalization flow, whereby any frequency dependence is avoided. The approach is illustrated in detail for a model of spinless fermions with nearest neighbour repulsion in one dimension. Even though the fermionic degrees of freedom do not provide an easy starting point in one dimension very good results are obtained which agree well with the exact findings based on Bethe ansatz.