2021/04/30 by Meng-Yuan Li, Peng Ye
Physics and Astronomy · #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.104.235127
published as Phys. Rev. B 104, 235127 (2021) · See also: arXiv:1909.02814; Accepted by Phys. Rev. B
arxiv created 2021/12/13 · arxiv updated 2021/12/16
Generally, ``fracton'' topological orders are referred to as gapped phases that support point-like topological excitations whose mobility is, to some extent, restricted. In our previous work [Phys. Rev. B 101, 245134 (2020)], a large class of exactly solvable models on hypercubic lattices are constructed. In these models, spatially extended excitations possess generalized fracton-like properties: not only mobility but also deformability is restricted. As a series work, in this paper, we proceed further to compute ground state degeneracy (GSD) in both isotropic and anisotropic lattices. We decompose and reconstruct ground states through a consistent collection of subsystem ground state sectors, in which mathematical game ``coloring method'' is applied. Finally, we are able to systematically obtain GSD formulas (expressed as log2 GSD) which exhibit diverse kinds of polynomial dependence on system sizes. For example, the GSD of the model labeled as [0,1,2,4] in four dimensional isotropic hypercubic lattice shows 12L2-12L+4 dependence on the linear size L of the lattice. Inspired by existing results [Phys. Rev. X 8, 031051 (2018)], we expect that the polynomial formulas encode geometrical and topological fingerprints of higher-dimensional manifolds beyond toric manifolds used in this work. This is left to future investigation.