近日，爱尔兰都柏林圣三一学院的Jamil Khalouf-Rivera及其研究团队取得一项新进展。经过不懈努力，他们揭示了二能级玻色子模型激发态量子相变中的简并及其对系统动力学的影响。相关研究成果已于2024年6月18日在国际知名学术期刊《物理评论A》上发表。

该研究团队深入分析了具有u(n+1)动力学代数的两能级玻色子模型中简并现象对模型尺寸的依赖关系，其中n代表集体自由度的数目。研究发现，在模型的ESQPT（激发态量子相变）临界能量以下，随着系统尺寸的增加，属于不同对称区域的相邻能级之间的能隙逐渐趋近于零。

研究人员详细解释了这种能隙趋于零的方式与集体自由度数量n的关系。对于只有一个集体自由度的系统（n=1），这一能隙会以指数方式迅速减小至零；而在具有多个自由度（n>1）的模型中，能隙的减小则呈现代数方式。结果表明，在n=1的有限系统中，非时序关联子的无限时间平均值是ESQPT序参数，而在n>1的系统中，该平均值仅在平均场极限下作为序参数起作用。

据悉，激发态量子相变(ESQPTs)强烈影响集体多体量子系统的光谱特性，改变不同量子相的简并模式。能级简并反过来影响系统的动力学。

附:英文原文

Title: Degeneracy in excited-state quantum phase transitions of two-level bosonic models and its influence on system dynamics

Author: Jamil Khalouf-Rivera, Qian Wang, Lea F. Santos, José-Enrique García-Ramos, Miguel Carvajal, Francisco Pérez-Bernal

Issue&Volume: 2024/06/18

Abstract: Excited-state quantum phase transitions (ESQPTs) strongly influence the spectral properties of collective many-body quantum systems, changing degeneracy patterns in different quantum phases. Level degeneracies in turn affect the system's dynamics. We analyze the degeneracy dependence on the size of two-level boson models with a u(n+1) dynamical algebra, where n is the number of collective degrees of freedom. Below the ESQPT critical energy of these models, the energy gap between neighboring levels that belong to different symmetry sectors gets close to zero as the system size increases. We report and explain why this gap goes to zero exponentially for systems with one collective degree of freedom but algebraically in models with more than one degree of freedom. As a consequence, we show that the infinite-time average of out-of-time-order correlators is an ESQPT order parameter in finite systems with n=1, but in systems with n>1, this average only works as an order parameter in the mean-field limit.

DOI: 10.1103/PhysRevA.109.062219

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.109.062219