Metal-insulator transition in an one-dimensional half-filled interacting mesoscopic ring with spinless fermions: Exact results

TL;DR

This paper investigates the metal-insulator transition in a one-dimensional half-filled interacting fermionic ring, using exact numerical methods to analyze persistent current and conductivity across different fillings and disorder levels.

Contribution

It provides exact results on the metal-insulator transition in a 1D fermionic ring with Coulomb interactions, highlighting the role of filling and correlation strength.

Findings

Metal-insulator transition occurs at half-filling with increasing U.

No transition observed away from half-filling even at large U.

Persistent current and Drude weight used to characterize conducting behavior.

Abstract

We calculate persistent current of one-dimensional rings of fermions neglecting the spin degrees of freedom considering only nearest-neighbor Coulomb interactions with different electron fillings in both ordered and disordered cases. We treat the interaction exactly and find eigenenergies by exact diagonalization of many-body Hamiltonian and compute persistent current by numerical derivative method. We also determine Drude weight to estimate the conducting nature of the system. From our numerical results, we obtain a metal-insulator transition in half-filled case with increasing correlation strength U but away from half-filling no such transition is observed even for large U.