Density Matrix Approach to Local Hilbert Space Reduction

TL;DR

This paper introduces a density matrix method for reducing local Hilbert space size in complex quantum systems, demonstrated on a 1D electron-phonon model, achieving high accuracy with fewer phonon modes.

Contribution

It develops a density matrix approach that efficiently reduces local degrees of freedom, enabling accurate simulations with fewer basis states.

Findings

Two or three optimized phonon modes per site match results with 10-100 bare phonon levels

The method improves computational efficiency for large or infinite local Hilbert spaces

Accurate results are obtained for the 1D Holstein model using the proposed approach

Abstract

We present a density matrix approach for treating systems with a large or infinite number of degrees of freedom per site with exact diagonalization or the density matrix renormalization group. The method is demonstrated on the 1D Holstein model of electrons coupled to Einstein phonons. In this system, two or three optimized phonon modes per site give results as accurate as with 10-100 bare phonon levels per site.