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

Physics – Condensed Matter – Strongly Correlated Electrons

Scientific paper

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6 Pages, Revtex, final version

Scientific paper

10.1209/epl/i1999-00171-0

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.

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