Researchers have introduced a new class of quantum states, termed 1-form symmetric projected entangled-pair states (PEPS). These states represent a generalization of traditional PEPS, incorporating a global symmetry that acts on the boundaries of the system in a specific manner. 1-form symmetry is a concept that has gained relevance in theoretical physics, especially in the study of topological phases of matter and in field theories, and its application to PEPS opens new avenues for understanding and classifying complex quantum states.

The relevance of this proposal lies in its potential to describe phases of matter with non-trivial topological orders, which are of great interest in condensed matter physics. PEPS are a powerful tool for simulating two-dimensional many-body quantum systems, and the addition of 1-form symmetry allows for capturing properties that were previously inaccessible or difficult to characterize. This advance could facilitate the identification and study of new topological phases, as well as the understanding of their fundamental properties, such as the degeneracy of their ground states and the existence of excitations with anomalous statistics.

The construction of these 1-form symmetric PEPS involves a modification of the tensors that define the state, ensuring that the action of the symmetry is preserved at a local level. This approach offers a unified framework for describing a variety of quantum phenomena, from long-range entanglement to boundary properties in topological systems. It is expected that this new formulation will boost both theoretical research and numerical simulations, providing more precise tools to explore the vast landscape of many-body quantum states.