A Density Matrix Renormalization Group Approach to an Asymptotically Free Model with Bound States

TL;DR

This paper demonstrates the application of the Density Matrix Renormalization Group (DMRG) method to a 2D delta function potential model, achieving high accuracy in calculating bound states and ground state energies, with potential extensions to quantum field theory.

Contribution

The paper introduces a novel application of DMRG to a simple quantum mechanical model with asymptotic freedom and bound states, and discusses its generalization to high energy physics models.

Findings

High-accuracy ground state energy calculations

Effective separation of energy scales in DMRG

Comparison with Similarity RG method

Abstract

We apply the DMRG method to the 2 dimensional delta function potential which is a simple quantum mechanical model with asymptotic freedom and formation of bound states. The system block and the environment block of the DMRG contain the low energy and high energy degrees of freedom, respectively. The ground state energy and the lowest excited states are obtained with very high accuracy. We compare the DMRG method with the Similarity RG method and propose its generalization to field theoretical models in high energy physics.