Thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model
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| Format: | Preprint |
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2025
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| _version_ | 1866911708863266816 |
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| author | Yu, Shengjie Zhu, Zhaoxuan Sanchez-Palencia, Laurent |
| author_facet | Yu, Shengjie Zhu, Zhaoxuan Sanchez-Palencia, Laurent |
| contents | The one-dimensional hard rod model describes impenetrable bosons with finite diameter, extending the Lieb-Liniger model to systems with excluded volume interactions. Here, we investigate the thermodynamics of quantum HRs using Yang-Yang theory, path integral quantum Monte-Carlo calculations, and Luttinger liquid theory. We first discuss the behavior of characteristic thermodynamic quantities, exhibiting deviations to the Lieb-Liniger model for sufficiently high densities, with excellent agreement between analytical and numerical results. We then show that the hard rod model exhibits Tomonaga-Luttinger liquid behavior across a wide range of parameters, at zero and finite temperature, as unveiled by correlation functions. The Tomonaga-Luttinger parameter and thermal length can be extracted by fitting correlation functions to Tomonaga-Luttinger liquid theory, hence demonstrating a robust method for thermometry. This work provides a comprehensive study of strongly correlated hard rod systems at finite temperatures, with applications to quantum wires, spin chains, and ultracold atoms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_20376 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model Yu, Shengjie Zhu, Zhaoxuan Sanchez-Palencia, Laurent Strongly Correlated Electrons Quantum Gases Quantum Physics The one-dimensional hard rod model describes impenetrable bosons with finite diameter, extending the Lieb-Liniger model to systems with excluded volume interactions. Here, we investigate the thermodynamics of quantum HRs using Yang-Yang theory, path integral quantum Monte-Carlo calculations, and Luttinger liquid theory. We first discuss the behavior of characteristic thermodynamic quantities, exhibiting deviations to the Lieb-Liniger model for sufficiently high densities, with excellent agreement between analytical and numerical results. We then show that the hard rod model exhibits Tomonaga-Luttinger liquid behavior across a wide range of parameters, at zero and finite temperature, as unveiled by correlation functions. The Tomonaga-Luttinger parameter and thermal length can be extracted by fitting correlation functions to Tomonaga-Luttinger liquid theory, hence demonstrating a robust method for thermometry. This work provides a comprehensive study of strongly correlated hard rod systems at finite temperatures, with applications to quantum wires, spin chains, and ultracold atoms. |
| title | Thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model |
| topic | Strongly Correlated Electrons Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2505.20376 |