Quantum Renormalization Group for 1 Dimensional Fermion Systems

TL;DR

This paper introduces a modified renormalization group method that incorporates boundary conditions, improving the accuracy of ground state energy estimates and correlation functions in 1D fermion systems.

Contribution

A simple modification of the RG technique that accounts for boundary effects, enhancing accuracy in quantum lattice system analysis.

Findings

Higher accuracy in ground state energy estimation.

Good agreement of correlation functions with exact results.

Effective for both free and interacting fermion systems.

Abstract

Inspired by the superblock method of White, we introduce a simple modification of the standard Renormalization Group (RG) technique for the study of quantum lattice systems. Our method which takes into account the effect of Boundary Conditions(BC), may be regarded as a simple way for obtaining first estimates of many properties of quantum lattice systems. By applying this method to the 1-dimensional free and interacting fermion system, we obtain the ground state energy with much higher accuracy than the standard RG. We also calculate the density-density correlation function in the free-fermion case which shows good agreement with the exact result.