2025/11/12 by Li, Bo-Xi, Ye, Peng · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2511.09301
Building on the recent study of Toeplitz braiding by Li et al. [Phys. Rev. B 110, 205108 (2024)], we introduce infinite-component BF (iBF) theories by stacking topological BF theories along a fourth (w) spatial direction and coupling them in a translationally invariant manner. The iBF framework captures the low-energy physics of 4D fracton topological orders in which both particle and loop excitations exhibit restricted mobility along the stacking direction, and their particle-loop braiding statistics are encoded in asymmetric, integer-valued Toeplitz K matrices. We identify a novel form of particle-loop braiding, termed Toeplitz braiding, originating from boundary zero singular modes (ZSMs) of the K matrix. In the thermodynamic limit, nontrivial braiding phases persist even when the particle and loop reside on opposite 3D boundaries, as the boundary ZSMs dominate the nonvanishing off-diagonal elements of K-1 and govern boundary-driven braiding behavior. Analytical and numerical studies of iBF theories with Hatano-Nelson-type and non-Hermitian Su-Schrieffer-Heeger-type Toeplitz K matrices confirm the correspondence between ZSMs and Toeplitz braiding. The iBF construction thus forges a bridge between strongly correlated topological field theory and noninteracting non-Hermitian physics, where ZSMs underlie the non-Hermitian amplification effect. Possible extensions include 3-loop and Borromean-rings Toeplitz braiding induced by twisted topological terms, generalized entanglement renormalization, and foliation structures within iBF theories. An intriguing analogy to the scenario of parallel universes is also briefly discussed.