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arXiv · 2306.00291

Ground State Degeneracy of Infinite-Component Chern-Simons-Maxwell Theories: Foliated vs. Non-foliated Fracton Orders

Xie Chen·Ho Tat Lam·Xiuqi Ma
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Abstract

Infinite-component Chern-Simons-Maxwell theories with a block-Toeplitz K matrix provide a vast landscape of gapped and gapless, foliated and non-foliated fracton orders. In this paper, we investigate the ground state degeneracy (GSD) of these theories, classifying distinct behaviors of the GSD as a function of the linear system size, i.e. the size of the K matrix. We find that the GSD can exhibit exponential or polynomial growth, cyclic variations across a finite set of values, or erratic fluctuations within an exponential envelope. We relate these different patterns to the roots of the determinant polynomial - a Laurent polynomial associated with the block-Toeplitz K matrix. These roots also play a crucial role in determining whether the theory is gapped or gapless. In addition, we propose a necessary condition for a gapped infinite-component Chern-Simons-Maxwell theory to be a foliated fracton order, based on the porperties of the determinant polynomial.

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Xie Chen, Ho Tat Lam, Xiuqi Ma. 2023-06-01. Ground State Degeneracy of Infinite-Component Chern-Simons-Maxwell Theories: Foliated vs. Non-foliated Fracton Orders. https://arxiv.org/abs/2306.00291

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