Thermodynamics and excitations of the one-dimensional Hubbard model

We review fundamental issues arising in the exact solution of the one-dimensional Hubbard model. We perform a careful analysis of the Lieb-Wu equations, paying particular attention to the so-called 'string solutions'. Two kinds of string solutions occur: Lambda strings, related to spin degrees of freedom and k-Lambda strings, describing spinless bound states of electrons. Whereas Lambda strings were thoroughly studied in the literature, less is known about k-Lambda strings. We carry out a thorough analytical and numerical 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 the 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 of the Yang-Yang approach. (C) 2000 Elsevier Science B.V. All rights reserved.