Matrix Product Approach to Conjugated Polymers

TL;DR

This paper applies the Matrix Product method to study the ground state of conjugated polymers, achieving accurate energy estimates and analyzing parameter evolution across different regimes.

Contribution

It extends the Matrix Product approach to conjugated polymers using the valence bond basis, incorporating symmetries and comparing results with DMRG.

Findings

Ground state energy per monomer computed with 2-4% accuracy compared to DMRG.

Demonstrated evolution of variational parameters in different dimerization regimes.

Validated the applicability of MPM to conjugated polymer systems.

Abstract

The Matrix Product method (MPM) has been used in the past to generate variational ansatzs of the ground state (GS) of spin chains and ladders. In this paper we apply the MPM to study the GS of conjugated polymers in the valence bond basis, exploiting the charge and spin conservation as well as the electron-hole and spin-parity symmetries. We employ the $U-V-\delta$ Hamiltonian which is a simplified version of the PPP Hamiltonian. For several coupling constants $U$ and $V$ and dimerizations $\delta$ we compute the GS energy per monomer which agrees within a $2%-4%$ accuracy with the DMRG results. We also show the evolution of the MP-variational parameters in the weak and strong dimerization regimes.