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.
Highlights
The celebrated Noether theorem relates a conservation law to an underlying continuous symmetry
One advantage of such an emergent higher rank symmetry is its robustness against symmetry-breaking perturbation. We expect that such a scenario holds promise for more flexible realization of exotic higher rank symmetry and higher moment conservation in both theoretical and experimental studies. We identify such a wide phase region that supports emergent higher rank symmetry and conservation of angular moments, i.e., d2xρ × x = d2x(ρ1x2 − ρ2x1) for a two-component boson field in two dimensions
We identify them as emergent phenomena rather than strict properties of microscopic models
Summary
The celebrated Noether theorem relates a conservation law to an underlying continuous symmetry. (2-dimensional particle) that are movable within a stack of parallel planes Regarding these strange particles as bosons, we can consider their Bose-Einstein condensation, such that the spontaneous breaking of higher rank symmetry occurs. One may wonder whether it is possible that the long-wavelength low-energy limit will conserve higher moments and respect higher rank symmetry as an emergent phenomenon. For this purpose, we may apply the traditional theoretical approach: renormalization group (RG). We identify such a wide phase region that supports emergent higher rank symmetry and conservation of angular moments, i.e., d2xρ × x = d2x(ρ1x2 − ρ2x1) for a two-component boson field in two dimensions. IV, we summarize and provide our prediction on conditions of possible realization of systems with higher rank symmetry
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