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

doi:10.1007/s11467-022-1186-x

Front. Phys.

2022, Vol. 17

Issue (6) : 61501 https://doi.org/10.1007/s11467-022-1186-x

RESEARCH ARTICLE

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

Ming-Cheng Liang^1,², Zhi-Xing Lin¹, Yang-Yang Chen^3,⁴, Xi-Wen Guan^3,⁵, Xibo Zhang^1,^2,⁶(

)

¹. International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China
². Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
³. State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
⁴. Institute of Modern Physics, Northwest University, Xi'an 710127, China
⁵. Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra ACT 0200, Australia
⁶. Beijing Academy of Quantum Information Sciences, Beijing 100193, China

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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.

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

Corresponding Author(s): Xibo Zhang

Issue Date: 15 July 2022

Cite this article:

Ming-Cheng Liang,Zhi-Xing Lin,Yang-Yang Chen, et al. Power-law scalings in weakly-interacting Bose gases at quantum criticality[J]. Front. Phys. , 2022, 17(6): 61501.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1186-x
https://academic.hep.com.cn/fop/EN/Y2022/V17/I6/61501

Fig.1 Critical entropy per particle as a function of scaled interaction strength

g ~ 1 D

. (a) Critical entropy per particle

S c / N

as a function of scaled interaction strength

g ~ 1 D = c / T

. Exact solutions (circles) agree well with the strong interaction limit

A ∞, 1 D

(dashed line). Here the error bars are much smaller than the symbols. (b) A power-law scaling of

S c / N

with respect to

g ~ 1 D

. A blue line shows a power-law scaling with an exponent of

1 / 3

, which agrees excellently with the exact solutions, as shown over a large range of

g ~ 1 D

Fig.2 Running power-law scaling exponent as a function of scaled interaction strength. As

g ~ 1 D

decreases towards zero, the running exponent

β R

approaches

1 / 3

from below. Uncertainties are quoted as

1 σ

standard errors.

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