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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 |
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Abstract 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.
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Received: 31 October 2023
Revised: 25 December 2023
Accepted manuscript online: 24 January 2024
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PACS:
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02.30.Jr
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(Partial differential equations)
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07.07.Df
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(Sensors (chemical, optical, electrical, movement, gas, etc.); remote sensing)
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07.05.Dz
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(Control systems)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12104372, 12047511, and 12247103) and the Youth Innovation Team of Shaanxi Universities. |
Corresponding Authors:
Song Cheng, Yang-Yang Chen
E-mail: scheng@csrc.ac.cn;chenyy@nwu.edu.cn
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Cite this article:
Xiao-Min Zhang(张小敏), Song Cheng(程颂), and Yang-Yang Chen(陈洋洋) Thermal-contact capacity of one-dimensional attractive Gaudin—Yang model 2024 Chin. Phys. B 33 040203
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