A H³(G,\mathbb T)-valued index of symmetry protected topological phases with on-site finite group symmetry for two-dimensional quantum spin systems

2021/01/02 by Yoshiko Ogata, Ogata, Yoshiko · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Topological Materials and Phenomena #cond-mat.stat-mech #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.2101.00426

The present result and the main idea of the proof were announced publicly on 15 Dec 2020 at IAMP One World Mathematical Physics Seminar (see you-tube video https://youtu.be/cXk6Fk5wD_4), also at an international meeting Theoretical studies of topological phases of matter on 17 Dec 2020, and Current Developments in Mathematics 4th Jan 2021 via zoom with a lecture note

openalex publication_date 2021/01/02 · arxiv created 2021/01/07 · arxiv updated 2021/01/08 · openalex created_date 2021/01/18 · openalex updated_date 2026/07/28

Abstract

We consider SPT-phases with on-site finite group G symmetry β for two-dimensional quantum spin systems. We show that they have H³(G,\mathbb T)-valued invariant.

Cited by

• The Lieb-Robinson condition and the Fréchet topology
• On Symmetry-Compatible Superselection Structures for Product States in 2D Quantum Spin Systems
• LSM and CPT
• Reflection positivity and a refined index for 2d invertible phases

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