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arXiv · 2507.03270

Soft breaking of the $\mathbb{Z}_2$ symmetry in the $\phi^4$ theory

F. C. E. Lima·C. A. S. Almeida
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Abstract

We consider a two-dimensional scalar field theory that modifies the standard $\phi^4$ model by introducing a smooth breaking of translational invariance through a hyperbolic generalizing function. This function explicitly breaks the $\mathbb{Z}_2$ symmetry; however, it also introduces a mechanism capable of generating new energy minima (vacua) and of localizing or delocalizing field fluctuations around these vacua. Thus, this mechanism enables the continuous transformation of the kink/antikink-like configurations into compacted asymmetric double-kink/antikink structures. Accordingly, this transformation gives rise to new classes of configurations resembling asymmetric non-topological solitons, characterized by a soft breaking of the $\mathbb{Z}_2$ symmetry. These findings are particularly compelling, as they are consistent with results describing Su-Schrieffer-Heeger (SSH) domain walls in dimerized polymer systems.

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F. C. E. Lima, C. A. S. Almeida. 2025-07-04. Soft breaking of the $\mathbb{Z}_2$ symmetry in the $\phi^4$ theory. https://arxiv.org/abs/2507.03270

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