Topological phases and spontaneous symmetry breaking: the revenge of the original Su-Schrieffer-Heeger model

Polina Matveeva; Dmitri Gutman; Sam T. Carr

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arXiv · 2508.01985

Topological phases and spontaneous symmetry breaking: the revenge of the original Su-Schrieffer-Heeger model

Polina Matveeva·Dmitri Gutman·Sam T. Carr

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Abstract

We study the interplay of spontaneous symmetry breaking and topological properties in interacting one-dimensional models. We solve these models using bozonization and identify topologically non-trivial phases by counting the additional degeneracy (affiliated with the edge modes) of a finite-size system relative to the infinite one. We find even if the mean-field solution is topological, this may not be true when it arises from spontaneous symmetry breaking, including in the Su-Schrieffer-Heeger (SSH) model. This implies that the original SSH model, as presented by Su, Schrieffer, and Heeger, is topologically trivial, as opposed to its mean-field version. A spinful version, on the other hand, does exhibit a topologically non-trivial phase. In that state, both mean-field solutions are topologically non-trivial and correspond to non-interacting SSH chains in the opposite phases with the winding number $\nu=1$. We show that this phase is protected by a chiral symmetry, similar to the non-interacting phases.

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Polina Matveeva, Dmitri Gutman, Sam T. Carr. 2025-08-04. Topological phases and spontaneous symmetry breaking: the revenge of the original Su-Schrieffer-Heeger model. https://arxiv.org/abs/2508.01985

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