Spin of the ground state and the flux phase problem on the ring

TL;DR

This paper investigates the optimal magnetic flux configuration that minimizes ground state energy in one-dimensional many-particle systems with odd particle numbers, exploring the connection between flux and ground state spin.

Contribution

It derives the optimal flux phase for energy minimization and analyzes the relationship between flux and ground state spin in one-dimensional systems.

Findings

Identifies the flux phase that minimizes ground state energy for odd particle systems.

Provides insights into the connection between flux and ground state spin.

Analyzes eigenvalue sums of one-particle Hamiltonians related to the flux.

Abstract

As a continuation of our previous work, we derive the optimal flux phase which minimizes the ground state energy in the one-dimensional many particle systems, when the number of particles is odd in the absence of on-site interaction and external potential. Moreover, we study the relationship between the flux on the ring and the spin of the ground state through which we derive some information on the sum of the lowest eigenvalues of one-particle Hamiltonians.