Pré-Publication, Document De Travail Année : 2025

Duality symmetry, zero energy modes and boundary spectrum of the sine-Gordon/massive Thirring model

Parameshwar R Pasnoori
  • Fonction : Auteur
Ari Mizel
  • Fonction : Auteur

Résumé

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 ($\widehat{\text{OBC}}$). The system exhibits a duality symmetry which relates models with opposite bare mass parameters and boundary conditions, i.e: $m_0 \leftrightarrow - m_0$, $\text{OBC}\leftrightarrow\widehat{\text{OBC}}$. For $m_0<0$ 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 $m_0<0$ and $\widehat{\text{OBC}}$, 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 $m_0>0$ and $\widehat{\text{OBC}}$, the trivial phase occurs, whereas the topological phase occurs for $m_0>0$ 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.

Dates et versions

hal-05016825 , version 1 (02-04-2025)

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Parameshwar R Pasnoori, Ari Mizel, Patrick Azaria. Duality symmetry, zero energy modes and boundary spectrum of the sine-Gordon/massive Thirring model. 2025. ⟨hal-05016825⟩
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