Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models

• URL: http://arxiv.org/abs/2104.05735v2
• Date: Mon, 13 Dec 2021 17:07:15 GMT
• Title: Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Authors: Meng-Yuan Li and Peng Ye
• Abstract summary: We decompose ground state degeneracy (GSD) in both isotropic and anisotropic lattices. We are able to systematically obtain GSD formulas which exhibit diverse kinds of dependence on system sizes.
• Score: 8.527114922918168
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Generally, ``fracton'' topological orders are referred to as gapped phases that support \textit{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, \textit{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 $\log_2 GSD$) 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 $ 12L^2-12L+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.

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