We investigate two-dimensional compactifications of three-dimensional fractonic stabilizer models. We find the two-dimensional topological phases produced as a function of compactification radius for the $X$ -cube model and Haah's cubic code. Furthermore, we uncover translation symmetry enrichment in the compactified cubic code that leads to twisted boundary conditions.We investigate two-dimensional compactifications of three-dimensional fractonic stabilizer models. We find the two-dimensional topological phases produced as a function of compactification radius for the $X$-cube model and Haah's cubic code. Furthermore, we uncover translation symmetry enrichment in the compactified cubic code that leads to twisted boundary conditions.

arXiv:1903.12246Physical review. B./Physical review. BJun 19, 201940 citations

Fracton phases via exotic higher-form symmetry-breaking

Marvin Qi, Leo Radzihovsky, Michael Hermele

arXiv:2010.02254Annals of PhysicsNov 25, 202085 citations

Fractonic matter in symmetry-enriched U(1) gauge theory

Dominic J. Williamson, Zhen Bi, Meng Cheng

This study reveals the relation between symmetry restrictions on the mobility of quasiparticles and symmetry-enriched topological order, where the actions of translation and global symmetries on quasiparticle excitations do not commute. The approach is demonstrably fruitful as one can systematically classify $U$ (1) gauge theories enriched by translation and certain global symmetry and identify new examples of fractonic matter. It is conjectured that all such theories can be constructed by gauging layered symmetry-protected topological phases.This study reveals the relation between symmetry restrictions on the mobility of quasiparticles and symmetry-enriched topological order, where the actions of translation and global symmetries on quasiparticle excitations do not commute. The approach is demonstrably fruitful as one can systematically classify $U$(1) gauge theories enriched by translation and certain global symmetry and identify new examples of fractonic matter. It is conjectured that all such theories can be constructed by gauging layered symmetry-protected topological phases.

arXiv:1809.10275Physical review. B./Physical review. BSep 23, 201986 citations

Non-Abelian defects in fracton phases of matter

Yizhi You

Fracton phases of matter host fractionalized topological quasiparticles with restricted mobility. A wide variety of fracton models with Abelian excitations had been proposed and extensively studied while the candidates for non-Abelian fracton phases are less explored. In this paper, we investigate the effect of twisted defects in Abelian fracton models. The twisted defect is launched by introducing a branch cut line hosting anyon condensate. In particular, these twisted defects, which alter different types of quasiparticles, carry projective non-Abelian zero modes. En route, such defects can be engineered via strong on-site hybridization along a branch cut which provides wide tunability and flexibility in experiment platforms. The braiding of twisted defects with projective non-Abelian Berry phases renders an avenue toward fault-tolerant quantum computation.Fracton phases of matter host fractionalized topological quasiparticles with restricted mobility. A wide variety of fracton models with Abelian excitations had been proposed and extensively studied while the candidates for non-Abelian fracton phases are less explored. In this paper, we investigate the effect of twisted defects in Abelian fracton models. The twisted defect is launched by introducing a branch cut line hosting anyon condensate. In particular, these twisted defects, which alter different types of quasiparticles, carry projective non-Abelian zero modes. En route, such defects can be engineered via strong on-site hybridization along a branch cut which provides wide tunability and flexibility in experiment platforms. The braiding of twisted defects with projective non-Abelian Berry phases renders an avenue toward fault-tolerant quantum computation.

arXiv:1901.07163Physical review. B./Physical review. BAug 26, 201911 citations

Chern-Simons-like theories for fracton phases

Weslei Bernardino Fontana

May 6, 20210 citations

X

-cube model and Haah's cubic code. Furthermore, we uncover translation symmetry enrichment in the compactified cubic code that leads to twisted boundary conditions.

U

(1) gauge theories enriched by translation and certain global symmetry and identify new examples of fractonic matter. It is conjectured that all such theories can be constructed by gauging layered symmetry-protected topological phases.