Charge-density-wave instabilities driven by multiple umklapp scattering

TL;DR

This paper generalizes the concept of umklapp-scattering driven instabilities in one-dimensional systems with longer-range interactions, using a new numerical method to analyze charge-density-wave instabilities in spinless fermions.

Contribution

It introduces a generalized framework for multiple umklapp-scattering processes at commensurate fillings and develops a new numerical approach to study ground-state susceptibilities.

Findings

Identifies conditions for charge-density-wave instabilities in 1D systems.

Develops a new method for calculating ground-state charge stiffness.

Demonstrates the role of longer-range interactions in driving instabilities.

Abstract

We show that the concept of umklapp-scattering driven instabilities in one-dimensional systems can be generalized to arbitrary multiple umklapp-scattering processes at commensurate fillings given that the system has sufficiently longer range interactions. To this end we study the fundamental model system, namely interacting spinless fermions on a one-dimensional lattice, via a density matrix renormalization group approach. The instabilities are investigated via a new method allowing to calculate the ground-state charge stiffness numerically exactly. The method can be used to determine other ground state susceptibilities in general.