Physics

This page summarizes my research activities in physics.

Research Works

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Haruki Yagi and Zongping Gong

Abstract
  • A rigorous analysis is presented for the entanglement spectrum of quantum many-body states possessing a higher-form group-representation symmetry generated by topological Wilson loops, which is generally non-invertible. A general framework based on elementary algebraic topology and category theory is developed to determine the block structure of reduced density matrices for arbitrary bipartite manifolds on which the states are defined. Within this framework, we scrutinize the impact of topology on the entanglement structure for low-dimensional manifolds, including especially the torus, the Klein bottle, and lens spaces. By further incorporating gauge invariance, we refine our framework to determine the entanglement structure for topological gauge theories in arbitrary dimensions. In particular, in two dimensions, it is shown for the Kitaev quantum double model that not only the topological entanglement entropy can be reproduced, but also the Li-Haldane conjecture concerning the full entanglement spectrum holds exactly.
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Haruki Yagi, Ken Mochizuki, and Zongping Gong

Abstract
  • A typical quantum state with no symmetry can be realized by letting a random unitary act on a fixed state, and the subsystem entanglement spectrum follows the Laguerre unitary ensemble (LUE). For integer-spin time reversal symmetry, we have an analogous scenario where we prepare a time-reversal symmetric state and let random orthogonal matrices act on it, leading to the Laguerre orthogonal ensemble (LOE). However, for half-integer-spin time reversal symmetry, a straightforward analogue leading to the Laguerre symplectic ensemble (LSE) is no longer valid due to that time reversal symmetric state is forbidden by the Kramers’ theorem. We devise a system in which the global time reversal operator is fractionalized on the subsystems, and show that LSE arises in the system. Extending this idea, we incorporate general symmetry fractionalization into the system, and show that the statistics of the entanglement spectrum is decomposed into a direct sum of LOE, LUE, and/or LSE. Here, various degeneracies in the entanglement spectrum may appear, depending on the non-Abelian nature of the symmetry group and the cohomology class of the non-trivial projective representation on the subsystem. Our work establishes the entanglement counterpart of the Dyson’s threefold way for Hamiltonians with symmetries.
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Others

To study conformal field theory (CFT) with friends, I organized and held CFT Camp. For details, please refer to the homepage (in Japanese).