Researchers have identified a new class of Lifshitz multicritical points in one-dimensional fermionic systems with chiral symmetry. This multicriticality, termed "topologically enforced," arises exclusively from changes in the topology of neighboring critical lines, distinguishing it from conventional multicritical points typically associated with variations in critical exponents. This finding expands the understanding of quantum phase transitions and universality classes beyond traditional paradigms of statistical and condensed matter physics.

The study focuses on the systematic construction and investigation of these multicritical points. Surprisingly, the topologically enforced multicriticality can host robust topological degeneracies. A remarkable aspect is that these systems exhibit a breakdown of the Li-Haldane bulk-boundary correspondence, a fundamental principle in topological physics that relates the properties of a material's interior to those of its surface or edge. The authors have provided a simple physical picture to elucidate this phenomenon.

This discovery suggests that topology plays an even richer role in determining the properties of quantum phase transitions. The ability to generate robust topological degeneracies at these multicritical points could have implications for the development of materials with novel quantum properties or for understanding complex quantum phenomena. The breakdown of the Li-Haldane bulk-boundary correspondence opens new avenues of research into the limits and applicability conditions of this principle.