Gapped lineon and fracton models on graphs

Journal Article · 08 March 2023 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.107.125121 · OSTI ID:2222884

Gorantla, Pranay  ^[1]; Lam, Ho Tat  ^[2]; Seiberg, Nathan  ^[3]; Shao, Shu-Heng  ^[4]

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1. Princeton University, NJ (United States); Institute for Advanced Study
2. Massachusetts Institute of Technology, Cambridge, MA (United States)
3. Institute for Advanced Study, Princeton, NJ (United States)
4. Stony Brook University, NY (United States)

We introduce a $$\mathbb{Z}_N$$ stabilizer code that can be defined on any spatial lattice of the form $$\Gamma\times C_{L_z}$$, where $$\Gamma$$ is a general graph. We also present the low-energy limit of this stabilizer code as a Euclidean lattice action, which we refer to as the anisotropic $$\mathbb{Z}_N$$ Laplacian model. It is gapped, robust (i.e., stable under small deformations), and has lineons. Its ground state degeneracy (GSD) is expressed in terms of a "mod $$N$$-reduction" of the Jacobian group of the graph $$\Gamma$$. In the special case when space is an $$L\times L\times L_z$$ cubic lattice, the logarithm of the GSD depends on $$L$$ in an erratic way and grows no faster than $O(L)$. Furthermore, we also discuss another gapped model, the $$\mathbb{Z}_N$$ Laplacian model, which can be defined on any graph. It has fractons and a similarly strange GSD.

• Research Organization: Institute for Advanced Study, Princeton, NJ (United States)
• Sponsoring Organization: USDOE; National Science Foundation (NSF)
• Grant/Contract Number: SC0009988
• OSTI ID: 2222884
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 12 Vol. 107; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English