高阶对称性和高阶矩守恒出现的重整化群分析
Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
摘要：
高阶对称性和高阶矩守恒已经引起了相当大的关注，例如，分形拓扑序的次扩散输运。在本文中，我们进行了一个单圈的重整化群（RG）分析，并显示这些现象是如何出现在低能量。我们考虑了d分量相互作用玻色子的$d$维模型。在具有守恒角动量的高阶对称点处，$a$次玻色子仅具有沿$x^a$方向的动能。因此，对称点看起来高度各向异性和微调。通过研究RG在一个广泛的附近的对称点，我们发现，不允许的动力学项往往是无关紧要的微扰制度，这可能会导致紧急高阶对称性和高矩守恒在深红外极限。虽然非微扰分析是在未来的要求，通过考虑高秩对称性作为一种新兴的现象，RG分析在本文中提出了实现高秩对称性和高矩守恒实验可实现的系统的替代承诺。
英文摘要：
Higher rank symmetry and higher moment conservation have been drawn considerable attention from, e.g., subdiffusive transport to fracton topological order. In this paper, we perform a one-loop renormalization group (RG) analysis and show how these phenomena emerge at low energies. We consider a $d$-dimensional model of interacting bosons of d components. At higher-rank-symmetric points with conserved angular moments, the $a$-th bosons have kinetic energy only along the $x^a$ direction. Therefore, the symmetric points look highly anisotropic and fine-tuned. By studying RG in a wide vicinity of the symmetric points, we find that symmetry-disallowed kinetic terms tend to be irrelevant within the perturbative regime, which potentially leads to emergent higher-rank symmetry and higher-moment conservation at the deep infrared limit. While non-perturbative analysis is called for in the future, by regarding higher-rank symmetry as an emergent phenomenon, the RG analysis presented in this paper holds alternative promise for realizing higher-rank symmetry and higher-moment conservation in experimentally achievable systems.
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