Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation

TL;DR

This paper uses one-loop renormalization group analysis to demonstrate how higher-rank symmetries and higher moment conservation can emerge at low energies in a model of interacting bosons, highlighting their potential realization in experiments.

Contribution

It provides a perturbative RG framework showing the emergence of higher-rank symmetries near symmetric points in bosonic systems, which was not previously established.

Findings

Symmetry-disallowed kinetic terms become irrelevant near symmetric points.

Emergent higher-rank symmetry and moment conservation are possible at low energies.

The analysis suggests experimental systems could realize these phenomena.

Abstract

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.