2023/06/01 by Xie Chen, Chen, Xie, Ho Tat Lam +3 · 1 citation
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Algebraic structures and combinatorial models #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2306.00291
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.