Those excited states of a half filled 1-d Hubbard chain are studied which are connected with electron pairs occupying the same sites. It is argued, that these states are to be described by such solutions of the Lieb-Wu equations in which some of the wavenumbers are complex. Solutions of this 2 type, corresponding to S = 1/2N-1 and singlet states are found. The energymomentum dispersion is also calculated. The gap in the spectrum of the singlet excitations is found to be equal to the discontinuity of the chemical potential calculated by Lieb and Wu. АННОТАЦИЯ Исследуются возбужденные состояния полузаполненных Хуббард-цепей, кото рые связаны с электронными парами, занимающими одинаковое место. Показано, что эти состояния описываются решениями уравнения ЛИБ-ВУ, содержащими комп лексные волновые векторы. Найдены решения уравнения ЛИБ-ВУ, содержащие одну пару комплексных волновых векторов, соответствующие Sz = 1/2 N-1 и синглетному спиновым состояниям. В обоих случаях определяются дисперсионные соотно шения энергии-импульса. "Gap" в спектре синглетных возбуждений соответствует скачку химического потенциала, вычисленному Либ и By. KIVONAT A félig töltött Hubbard láncok azon gerjesztett állapotait vizsgáljuk, amelyek azonos rácshelyet elfoglaló elektron-párokkal kapcsolatosak. Megmu tatjuk, hogy ezeket az állapotokat a Lieb-Wu egyenletek komplex hullámszámot is tartalmazó megoldásai Írják le. Megkeressük a Lieb-Wu egyenletek z " S = 1/2N-1 és singlet spinállapotoknak megfelelő egy komplex hullámszam-párt tartalmazó megoldásait. Mindkét esetre meghatározzuk az energia-momentum diszperziót is. A singlet gerjesztések spektrumában található gap azonos a kémiai potenciál Lieb és Wu által kiszámolt ugrásával.
Leading and next-to-leading-order finite-size corrections to the ground and first excited states are calculated for the spin-1/2 anisotropic Heisenberg model in the critical region. The analytic results are compared to numerical data obtained for chains up to a length of N=1024. It is found that, near the isotropic point, the asymptotic region where the results obtained for N to infinity are applicable sets in at very large N values, and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms, even at large (N>100) chain lengths.
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