On the lowest energy excitations of one-dimensional strongly correlated electrons

TL;DR

This paper proves that the lowest energy excitations in certain one-dimensional strongly correlated electron models are periodic functions of momentum, with implications for their spectral gap properties depending on magnetic ground states.

Contribution

It establishes the periodicity and gapless conditions of low-energy excitations in one-dimensional strongly correlated electron models, extending understanding of their spectral properties.

Findings

Lowest excitations are π-periodic functions of momentum.

At fractional fillings, excitations satisfy a specific periodicity related to electron density.

Systems with magnetic ground states are gapless at all wave vectors.

Abstract

It is proven that the lowest excitations $E_{low}(k)$ of one-dimensional half-integer spin generalized Heisenberg models and half-filled extended Hubbard models are $\pi$-periodic functions. For Hubbard models at fractional fillings $E_{low}{(k+ 2 k_f)} = E_{low}(k)$, where $2 k_f= \pi n$, and $n$ is the number of electrons per unit cell. Moreover, if one of the ground states of the system is magnetic in the thermodynamic limit, then $E_{low}(k) = 0$ for any $k$, so the spectrum is gapless at any wave vector. The last statement is true for any integer or half-integer value of the spin.