Equivariant parameter families of spin chains: A discrete MPS formulation, by Ken Shiozaki

SciPost Physics Home Authoring Refereeing Submit a manuscript About Equivariant parameter families of spin chains: A discrete MPS formulation Ken Shiozaki SciPost Phys. 20, 024 (2026) · published 28 January 2026 doi: 10.21468/SciPostPhys.20.1.024 pdf BiBTeX RIS Submissions/Reports Abstract We analyze topological phase transitions and higher Berry curvature in one-dimensional quantum spin systems, using a framework that explicitly incorporates the symmetry group action on the parameter space. Based on a $G$-compatible discretization of the parameter space, we incorporate both group cochains and parameter-space differentials, enabling the systematic construction of equivariant topological invariants. We derive a fixed-point formula for the higher Berry invariant in the case where the symmetry action has isolated fixed points. This reveals that the phase transition point between Haldane and trivial phases acts as a monopole-like defect where higher Berry curvature emanates. We further discuss hierarchical structures of topological defects in the parameter space, governed by symmetry reductions and compatibility with subgroup structures. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.1.024TI - Equivariant parameter families of spin chains: A discrete MPS formulationPY - 2026/01/28UR - https://scipost.org/SciPostPhys.20.1.024JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 1SP - 024A1 - Shiozaki, KenAB - We analyze topological phase transitions and higher Berry curvature in one-dimensional quantum spin systems, using a framework that explicitly incorporates the symmetry group action on the parameter space. Based on a $G$-compatible discretization of the parameter space, we incorporate both group cochains and parameter-space differentials, enabling the systematic construction of equivariant topological invariants. We derive a fixed-point formula for the higher Berry invariant in the case where the symmetry action has isolated fixed points. This reveals that the phase transition point between Haldane and trivial phases acts as a monopole-like defect where higher Berry curvature emanates. We further discuss hierarchical structures of topological defects in the parameter space, governed by symmetry reductions and compatibility with subgroup structures.ER - × @Article{10.21468/SciPostPhys.20.1.024, title={{Equivariant parameter families of spin chains: A discrete MPS formulation}}, author={Ken Shiozaki}, journal={SciPost Phys.}, volume={20}, pages={024}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.1.024}, url={https://scipost.org/10.21468/SciPostPhys.20.1.024},} Disclosure of Generative AI use The author(s) disclose that the following generative AI tools have been used in the preparation of this publication: Generative AI tools (OpenAI ChatGPT, July 2025) were used for English language editing and translation of parts of the manuscript. No AI tool was used for generating research content or results. Ontology / Topics See full Ontology or Topics database. Matrix product states (MPS) Topological invariants Topological phase transitions Author / Affiliation: mappings to Contributors and Organizations See all Organizations. 1 Ken Shiozaki 1 京都大学 / Kyoto University Funders for the research work leading to this publication Japan Science and Technology Agency [JST] 日本学術振興会 / Japan Society for the Promotion of Science [JSPS]