Thermodynamics and excitations of the one-dimensional Hubbard model

We review fundamental issues arising in the exact solution of the one-dimen sional Hubbard model. We perform a careful analysis of the Lieb-Wu equation s, paying particular attention to the so-called 'string solutions'. Two kin ds of string solutions occur: Lambda strings, related to spin degrees of fr eedom and k-Lambda strings, describing spinless bound states of electrons. Whereas Lambda strings were thoroughly studied in the literature, less is k nown about k-Lambda strings. We carry out a thorough analytical and numeric al analysis of k-Lambda strings. We further review two different approaches to the thermodynamics of the Hubbard model, the Yang-Yang approach and the quantum transfer matrix approach, respectively. The Yang-Yang approach is based on strings, the quantum transfer matrix approach is not. We compare t he results of both methods and show that they agree. Finally, we obtain the dispersion curves of all elementary excitations at zero magnetic field for the less than half-filled band by considering the zero-temperature limit o f the Yang-Yang approach. (C) 2000 Elsevier Science B.V. All rights reserve d.