中国物理B ›› 2024, Vol. 33 ›› Issue (4): 40203-040203.doi: 10.1088/1674-1056/ad21f4
Thermal-contact capacity of one-dimensional attractive Gaudin—Yang model
Xiao-Min Zhang(张小敏)1, Song Cheng(程颂)2,†, and Yang-Yang Chen(陈洋洋)1,3,4,‡
- 1 Institute of Modern Physics, Northwest University, Xi'an 710069, China;
2 Beijing Computational Science Research Center, Beijing 100193, China;
3 Peng Huanwu Center for Fundamental Theory, Northwest University, Xi'an 710069, China;
4 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Northwest University, Xi'an 710069, China
Thermal-contact capacity of one-dimensional attractive Gaudin—Yang model
Xiao-Min Zhang(张小敏)1, Song Cheng(程颂)2,†, and Yang-Yang Chen(陈洋洋)1,3,4,‡
- 1 Institute of Modern Physics, Northwest University, Xi'an 710069, China;
2 Beijing Computational Science Research Center, Beijing 100193, China;
3 Peng Huanwu Center for Fundamental Theory, Northwest University, Xi'an 710069, China;
4 Shaanxi Key Laboratory for Theoretical Physics Frontiers, Northwest University, Xi'an 710069, China
摘要： Tan's contact $\mathcal{C}$ 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 $\mathcal{K}_{\scriptscriptstyle{\rm T}}$, i.e., the derivative of $\mathcal{C}$ with respect to temperature in the attractive Gaudin—Yang model. It is found that $\mathcal{K}_{\scriptscriptstyle{\rm T}}$ is useful in identifying the low temperature phase diagram, and using the obtained analytical expression of $\mathcal{K}_{\scriptscriptstyle{\rm T}}$, we study its critical behavior and the scaling law. Especially, we show $\mathcal{K}_{\scriptscriptstyle{\rm T}}$ versus temperature and thus the non-monotonic tendency of $\mathcal{C}$ 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.
中图分类号: (Partial differential equations)
- 02.30.Jr