2024/12/27 by Delcamp, Clement, Heng, Edmund, Yu, Matthew
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2412.19635
We investigate the action of a non-semisimple, non-invertible symmetry on spin chains, whose topological defects encode the category of modules over the Taft algebra of dimension 4. Sacrificing Hermiticity, we construct several symmetric, frustration-free, gapped Hamiltonians with real spectra and analyse their ground state subspaces. Our study reveals two intriguing phenomena. First, we identify an \mathbbS1-parametrised family of symmetric states, all of which belong to the same gapped phase with respect to the invertible subsymmetry, yet transform inequivalently under the non-semisimple symmetry. Second, we find a model where a product state and the so-called W state spontaneously break the symmetry. We further relate the indistinguishability of these two states in the infinite-volume limit to the notion that they are associated with a simple object and its projective cover, respectively, in a non-semisimple module category.