Correlation effects for semiconducting single wall carbon nanotube: a density matrix renormalization group study

TL;DR

This study applies the density matrix renormalization group method to analyze correlation effects in a specific semiconducting single wall carbon nanotube, revealing insights into its phase diagram and potential excitonic insulator state.

Contribution

It demonstrates the applicability of DMRG to the SWCN and explores the competition between Coulomb interactions affecting its ground states.

Findings

Calculated phase diagram for SWCN with specific chiral indices.

Identified possible correlated ground states and excitations.

Addressed the connection to excitonic insulator phenomena.

Abstract

In this paper, we report the applicability of the density matrix renormalization group(DMRG) approach to the cylindrical single wall carbon nanotube (SWCN) for purpose of its correlation effect. By applying the DMRG approach to the $t$+$U$+$V$ model, with $t$ and $V$ being the hopping and Coulomb energies between the nearest neighboring sites, respectively, and $U$ the onsite Coulomb energy, we calculate the phase diagram for the SWCN with chiral numbers ($n_{1}=3, n_{2}=2$), which reflects the competition between the correlation energy $U$ and $V$. Within reasonable parameter ranges, we investigate possible correlated groundstates, the lowest excitations and the corresponding correlation functions in which the connection with the excitonic insulator is particularly addressed.