東京大学 · 物理学・天文学
林浩教授の研究室では、対称性保護型トポロジカル相やギャップなしトポロジカル物質状態の理論的構築に注力しています。特に、ケネディ＝タサキ変換を非ユニタリな非可逆的双対性として一般化し、閉じたスピンチェーン上での対称性保護型トポロジカル秩序の構成を可能にしました。また、ギャップなしSPT状態の構成や、境界状態における準簡約性・対称性荷重の解析を通じて、非代替的トポロジカル秩序の理解を深めています。
Figures are computed from collected data and may differ slightly.
In 1992, Kennedy and Tasaki constructed a nonlocal unitary transformation that maps between a ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ spontaneously symmetry breaking phase and the Haldane gap phase, which is a prototypical symmetry-protected topological (SPT) phase in modern framework, on an open spin chain. In this work, we propose a way to define it on a closed chain by sacrificing unitarity. The operator realizing such a nonunitary transformation satisfies noninve
Symmetry protected topological (SPT) phases are one of the simplest, yet nontrivial, gapped systems that go beyond the Landau paradigm. In this work, we study an extension of the notion of SPT for gapless systems, namely, gapless symmetry protected topological states. We construct several simple gapless-SPT models using the decorated defect construction, which allow analytical understanding of non-trivial topological features including the symmetry charge under twisted boundary conditions, and b
The Kennedy-Tasaki (KT) transformation was used to construct the gapped symmetry protected topological (SPT) phase from the symmetry breaking phase with open boundary condition, and was generalized in our proceeding work [Phys. Rev. B 108, 214429 (2023)] on a ring by sacrificing the unitarity, and should be understood as a non-invertible duality transformation. In this work, we further apply the KT transformation to systematically construct gapless symmetry protected topological phases. This con
Symmetry protected topological (SPT) phases are one of the simplest, yet nontrivial, gapped systems that go beyond the Landau paradigm. In this work, we study an extension of the notion of SPT for gapless systems, namely, gapless symmetry protected topological states. We construct several simple gapless-SPT models using the decorated defect construction, which allow analytical understanding of non-trivial topological features including the symmetry charge under twisted boundary conditions, and b
We study a relationship between conformally invariant boundary conditions and anomalies of conformal field theories (CFTs) in $1+1$ dimensions. For a given CFT with a global symmetry, we consider symmetric ``gapping potentials'', which are relevant perturbations to the CFT. If a gapping potential is introduced only in a subregion of the system, it provides a certain boundary condition to the CFT. From this equivalence, if there exists a Cardy boundary state, which is invariant under a symmetry,
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