The non-perturbative constraints imposed by intrinsic fermionic non-invertible symmetries in 1+1 dimensional gapped systems remain largely unexplored. In this letter, we propose the superstrip algebra as a unified framework to catalog the categorical symmetry data in a massive fermionic model. The algebra and its representations explicitly encode the vacuum structure, soliton degeneracies, and their quantum numbers. As a demonstration, we apply this framework to the $\mathcal N=2$ minimal models with their least relevant deformation. We show that this specific deformation alone preserves a non-invertible superfusion category, a fermionic variant of $\text{SU}(2)_k$ known to underlie the $ADE$ classification of critical theories. Its superstrip algebra then accounts for the origin of the resulting $ADE$ -type soliton spectrum and their fractional fermion number. Although our primary examples are supersymmetric and integrable, our framework itself relies on neither property, providing a new powerful tool for studying a broad class of strongly-coupled fermionic systems.The non-perturbative constraints imposed by intrinsic fermionic non-invertible symmetries in 1+1 dimensional gapped systems remain largely unexplored. In this letter, we propose the superstrip algebra as a unified framework to catalog the categorical symmetry data in a massive fermionic model. The algebra and its representations explicitly encode the vacuum structure, soliton degeneracies, and their quantum numbers. As a demonstration, we apply this framework to the $\mathcal N=2$ minimal models with their least relevant deformation. We show that this specific deformation alone preserves a non-invertible superfusion category, a fermionic variant of $\text{SU}(2)_k$ known to underlie the $ADE$ classification of critical theories. Its superstrip algebra then accounts for the origin of the resulting $ADE$-type soliton spectrum and their fractional fermion number. Although our primary examples are supersymmetric and integrable, our framework itself relies on neither property, providing a new powerful tool for studying a broad class of strongly-coupled fermionic systems.

arXiv:2511.22129Nov 27, 20250 citations

Interacting fermions and interacting solitons

Bibhuti Bhusan Deo

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoApr 1, 19770 citations

Quantum-molecular-dynamics calculation of the density of states and electrical conductivity: application to the soliton model for polyacetylene

Kristel F. L. Michielsen, Hans A. De Raedt

We present a simulation method to compute the time-dependent properties of a system of fermions coupled to classical degrees of freedom. The method is employed to calculate the static and dynamic properties of the Su-Schrieffer-Heeger model for polyacetylene chains. Our results for the static quantities for chains, containing up to 256 electrons on 256 sites, are in excellent agreement with previous work and confirm that solitons are only present for very small doping. Our simulation data for the optical absorption as a function of dopant concentration are in good agreement with experiment.We present a simulation method to compute the time-dependent properties of a system of fermions coupled to classical degrees of freedom. The method is employed to calculate the static and dynamic properties of the Su-Schrieffer-Heeger model for polyacetylene chains. Our results for the static quantities for chains, containing up to 256 electrons on 256 sites, are in excellent agreement with previous work and confirm that solitons are only present for very small doping. Our simulation data for the optical absorption as a function of dopant concentration are in good agreement with experiment.

Europhysics Letters (EPL)May 20, 19965 citations

\mathcal N=2

minimal models with their least relevant deformation. We show that this specific deformation alone preserves a non-invertible superfusion category, a fermionic variant of

\text{SU}(2)_k

known to underlie the

ADE

classification of critical theories. Its superstrip algebra then accounts for the origin of the resulting

ADE

-type soliton spectrum and their fractional fermion number. Although our primary examples are supersymmetric and integrable, our framework itself relies on neither property, providing a new powerful tool for studying a broad class of strongly-coupled fermionic systems.