2025/03/18 by Parameshwar R. Pasnoori, Pasnoori, Parameshwar R., Ari Mizel +3 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2503.14776
openalex publication_date 2025/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We solve the one-dimensional massive Thirring model, which is equivalent to the one-dimensional sine-Gordon model, with two types of Dirchlet boundary conditions: open boundary conditions (OBC) and twisted open boundary conditions (\widehatOBC). The system exhibits a duality symmetry which relates models with opposite bare mass parameters and boundary conditions, i.e: m0 ↔ - m0, OBC↔\widehatOBC. For m0<0 and OBC, the system is in a trivial phase whose ground state is unique, as in the case of periodic boundary conditions. In contrast, for m0<0 and \widehatOBC, the system is in a topological phase characterized by the existence of zero energy modes (ZEMs) localized at each boundary. As dictated by the duality symmetry, for m0>0 and \widehatOBC, the trivial phase occurs, whereas the topological phase occurs for m0>0 and OBC. In addition, we analyze the structure of the boundary excitations, finding significant differences between the attractive (g>0) and the repulsive (g<0) regimes.