The magnetic properties of an attractive Hubbard chain are considered. Based on the Bethe Ansatz equations of the problem, exact analytic expressions are derived for the magnetization and susceptibility. These formulae can be evaluated after solving certain "derivatives" of the Bethe Ansatz equations. These derivative equations are also given. We give the magnetization and susceptibility curves for several values of the interaction-strength and bandfilling. We find that the susceptibility at the onset of magnetization (at the critical field) is finite for all bandfillings, except for the cases of half filled and empty bands, and in the limit of vanishing interaction. We argue that the finiteness of the initial susceptibility is due to the fermion-like behavior of the bound pairs. We also give the gap (what is equal to the critical field) and the initial susceptibility as functions of the interaction-strength and bandfilling for the cases of nearly half filled and almost empty bands as a function of the interaction, and in the weak coupling limit as a function of the bandfilling. To our knowledge, this is the first Bethe Ansatz calculation for the gap in this latter limit.
ASJC Scopus subject areas
- Condensed Matter Physics