TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.14.5.106
TI  - Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs
PY  - 2023/05/11
UR  - https://www.scipost.org/SciPostPhys.14.5.106
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 14
IS  - 5
SP  - 106
A1  - Ebisu, Hiromi
AU  - Han, Bo
AB  - We study unusual gapped topological phases where they admit $\mathbb{Z}_N$ fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on the local geometry of the system. Placing such phases on 2D lattice, composed of an arbitrary connected graph and 1D line, we find that the fusion rules of quasiparticle excitations are described by the Laplacian of the graph and that the number of superselection sectors is related to the kernel of the Laplacian. Based on this analysis, we further show that the ground state degeneracy is given by $\bigl[N\times \prod_{i}\text{gcd}(N, p_i)\bigr]^2$, where $p_i$'s are invariant factors of the Laplacian that are greater than one and gcd stands for the greatest common divisor. We also discuss braiding statistics between quasiparticle excitations.
ER  -

@Article{10.21468/SciPostPhys.14.5.106,
	title={{Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs}},
	author={Hiromi Ebisu and Bo Han},
	journal={SciPost Phys.},
	volume={14},
	pages={106},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.14.5.106},
	url={https://scipost.org/10.21468/SciPostPhys.14.5.106},
}