Symmetrized DMRG Method for Excited States of Hubbard Models

TL;DR

This paper introduces a symmetrized DMRG method that efficiently computes excited states of Hubbard models by exploiting symmetries, enabling accurate results for larger systems and opening avenues for studying optical properties of low-dimensional materials.

Contribution

The authors extend the DMRG method to incorporate parity, $C_2$, and electron-hole symmetries, improving its capability to analyze excited states in Hubbard models.

Findings

Accurately computed lowest energy states in all symmetry subspaces of Hubbard chains.

Ground-state energy, optical gap, and spin gap agree with exact results.

Method enables future studies of optical properties in low-dimensional systems.

Abstract

We extend the density matrix renormalization group method to exploit Parity, $C_2$ (rotation by $\pi$) and electron-hole symmtries of model Hamiltonians. We demonstrate the power of this method by obtaining the lowest energy states in all the eight symmetry subspaces of Hubbard chains with upto 50 sites. The ground-state energy, optical gap and spin gap of regular $U=4t$ and $U=6t$ Hubbard chains agree very well with exact results. This development extends the scope of the DMRG method and allows future applications to study of optical properties of low-dimensional conjugated polymeric systems.