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Topological and Many-body Localization Phases in Spinor Bose-Hubbard Models

Research Project

Project/Area Number 20J20715
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Review Section Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
Research InstitutionThe University of Tokyo

Principal Investigator

YANG Hong  東京大学, 理学系研究科, 特別研究員(PD)

Project Period (FY) 2020-04-24 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2022: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2021: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2020: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsemergent anomaly / SPT phase / SPT criticality / Kennedy-Tasaki / duality / SPT states / Ultracold atoms
Outline of Research at the Start

Interacting alkali atoms trapped in optical lattices serve as an ideal platform for realizing various quantum phases. We are especially interested in the exact results of the model Hamiltonians which exhibit symmetry-protected topological or many-body localization phases.

Outline of Annual Research Achievements

Previously, we revisited the Kennedy-Tasaki duality and revealed the KT duality provides a “hidden symmetry breaking” interpretation for the topological criticality. We also noticed that the KT self-duality is closely related to an emergent Lieb-Schultz-Mattis (LSM) anomaly.

However, the nature of the emergent LSM anomaly was not very clear to us before. Therefore, we focused on investigating the emergent anomaly. Using perturbation theory, we find that the low-energy theory of our spin-1 model near the critical self-dual point is equivalent to a spin-1/2 XYZ chain. This means that, near the self-dual point, the symmetry Z2y \rtimes Z2z × Ztrn of the complete theory reduces to Zy′ × Zz′ × Ztrn in the low-energy theory. In other words, in the low-energy theory, Z4y \rtimes Z2z × Ztrn leads to an LSM anomaly, which results in the absence of a unique gapped ground state. However, Z4y \rtimes Z4z × Ztrn in the spin-1 Hilbert space has no anomaly. In other words, the LSM anomaly around the self-dual point is actually emergent. Since the complete theory in the spin-1 Hilbert space is anomaly-free, the emergent anomaly has to be cancelled by some mechanism. Note that for the gapped symmetry Z2y, the nontrivial group element (π rotation) is identical to -1 in the low-energy theory. This indicates that the ground state is "stacked" on a gapped (weak) symmetry-protected topological (SPT) phase protected by Z2y × Ztrn. It is this SPT phase that cancels the emergent anomaly. We use field theory to demonstrate our argument.

* \rtimes means semi-direct product.

Research Progress Status

令和4年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和4年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2022 Annual Research Report
  • 2021 Annual Research Report
  • 2020 Annual Research Report
  • Research Products

    (8 results)

All 2023 2022 2021 2020

All Journal Article (2 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 2 results,  Open Access: 1 results) Presentation (6 results) (of which Int'l Joint Research: 2 results)

  • [Journal Article] Duality, criticality, anomaly, and topology in quantum spin-1 chains2023

    • Author(s)
      Yang Hong、Li Linhao、Okunishi Kouichi、Katsura Hosho
    • Journal Title

      Physical Review B

      Volume: 107 Issue: 12 Pages: 125158-125158

    • DOI

      10.1103/physrevb.107.125158

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Symmetry-protected topological phases in spinful bosons with a flat band2021

    • Author(s)
      Yang Hong、Nakano Hayate、Katsura Hosho
    • Journal Title

      Physical Review Research

      Volume: 3 Issue: 2 Pages: 023210-023210

    • DOI

      10.1103/physrevresearch.3.023210

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] Magnetic and Topological Phases of Spinful Bosons in Optical Lattices2022

    • Author(s)
      YANG HONG
    • Organizer
      Ultracold Atoms Japan 2022
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains2022

    • Author(s)
      YANG HONG
    • Organizer
      第17回量 子スピン系研究会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Magnetic and Topological Phases of Spinful Bosons in Optical Lattices2021

    • Author(s)
      YANG HONG
    • Organizer
      第3回冷却原子研究会「アトムの会」
    • Related Report
      2021 Annual Research Report
  • [Presentation] Criticality, duality, and topology in quantum spin-1 chains2021

    • Author(s)
      YANG HONG
    • Organizer
      日本物理学会2021年秋季大会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Symmetry-protected Topological Phases in Spinful Bosons with a Flat Band2021

    • Author(s)
      YANG HONG
    • Organizer
      American Physical Society March Meeting 2021
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Symmetry-protected Topological Phases in Spinful Bosons with a Flat Band2020

    • Author(s)
      YANG HONG
    • Organizer
      日本物理学会2020年秋季大会
    • Related Report
      2020 Annual Research Report

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Published: 2020-07-07   Modified: 2024-03-26  

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