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 KT , i.e., the derivative of C with respect to temperature in the attractive Gaudin–Yang model. It is found that KT is useful in identifying the low temperature phase diagram, and using the obtained analytical expression of KT , we study its critical behavior and the scaling law. Especially, we show KT 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.