Thermal-contact capacity of one-dimensional attractive Gaudin–Yang model

Abstract

Tan’s contact C is an important quantity measuring the two-body correlations at short distances in a dilute system. Here we make use of the technique of exactly solved models to study the thermal-contact capacity K T , i.e., the derivative of C with respect to temperature in the attractive Gaudin–Yang model. It is found that K T is useful in identifying the low temperature phase diagram, and using the obtained analytical expression of K T , we study its critical behavior and the scaling law. Especially, we show K T versus temperature and thus the non-monotonic tendency of C in a tiny interval, for both spin-balanced and imbalanced phases. Such a phenomenon is merely observed in multi-component systems such as SU(2) Fermi gases and spinor bosons, indicating the crossover from the Tomonaga–Luttinger liquid to the spin-coherent liquid.