Finite-Size Bosonization and Self-Consistent Harmonic Approximation

TL;DR

This paper extends the self-consistent harmonic approximation to include Klein factors in bosonized Hamiltonians, enabling accurate analysis of finite systems with interacting fermions, and compares results with exact solutions.

Contribution

It introduces a method to incorporate Klein factors into the harmonic approximation for finite systems, improving the analysis of bosonized Hamiltonians.

Findings

Finite-size corrections to energy gap calculated

Finite-size corrections to Drude weight obtained

Results agree with exact solutions for specific parameters

Abstract

The self-consistent harmonic approximation is extended in order to account for the existence of Klein factors in bosonized Hamiltonians. This is important for the study of finite systems where Klein factors cannot be ignored a priori. As a test we apply the method to interacting spinless fermions with modulated hopping. We calculate the finite-size corrections to the energy gap and the Drude weight and compare our results with the exact solution for special values of the model parameters.