Power-law scalings in weakly-interacting Bose gases at quantum criticality

Abstract

Weakly interacting quantum systems in low dimensions have been investigated for a long time, but there still remain a number of open questions and a lack of explicit expressions of physical properties of such systems. In this work, we find power-law scalings of thermodynamic observables in low-dimensional interacting Bose gases at quantum criticality. We present a physical picture for these systems with the repulsive interaction strength approaching zero; namely, the competition between the kinetic and interaction energy scales gives rise to power-law scalings with respect to the interaction strength in characteristic thermodynamic observables. This prediction is supported by exact Bethe ansatz solutions in one dimension, demonstrating a simple 1/3-power-law scaling of the critical entropy per particle. Our method also yields results in agreement with a non-perturbative renormalization-group computation in two dimensions. These results provide a new perspective for understanding many-body phenomena induced by weak interactions in quantum gases.

Graphical abstract

Keywords

power-law scaling / quantum criticality / Bose gases / weak interaction / non-perturbative methods

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Electronic supplementary materials

are available in the online version of this article at https://doi.org/10.1007/s11467-022-1186-x and https://journal.hep.com.cn/fop/EN/10.1007/s11467-022-1186-x and are accessible for authorized users.

Acknowledgements

This work was supported by the National Key Research and Development Program of China under Grant No. 2018YFA0305601, the National Natural Science Foundation of China under Grant No. 11874073, the Chinese Academy of Sciences Strategic Priority Research Program under Grant No. XDB35020100, and the Hefei National Laboratory and the Scientific and Technological Innovation 2030 under Grant No. 2021ZD0301903. X. W. Guan is supported by the National Natural Science Foundation of China under key Grant No. 12134015, and under Grants No. 11874393 and No. 12121004. Y. Y. Chen is supported by the National Natural Science Foundation of China under Grant No. 12104372.

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