[Seminar] Mr. Hong Yang "Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains"


Wednesday, April 20, 2022 - 15:00 to 16:00





Mr. Hong Yang
The University of Tokyo

Present: PhD candidate at Katsura group, Department of Physics, The University of Tokyo.
Mainly interested in symmetry-protected topological order.
2019: Master of Science, The University of Tokyo. Master thesis: Rigorous Results for the Ground States of Spinor Bose-Hubbard Models
2017: Bachelor of Science, Beijing Normal University.


Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains


The concept of duality plays a important role in physics, in particular in the study of quantum phases of matter. For example, in quantum spin-1 chains, there is a nonlocal unitary transformation, known as the Kennedy-Tasaki (KT) transformation, that defines a duality between the Haldane phase and the Z2×Z2 symmetry-breaking phase [1-3]. In our paper [4], we find that the KT transformation also defines a duality between a topological Ising critical phase and a trivial Ising critical phase, which provides a "hidden symmetry breaking" interpretation for the topological criticality. Moreover, since the duality relates different phases of matter, we argue that a model with self-duality (i.e., invariant under the KT transformation) is natural to be at a critical or multicritical point. We study concrete examples to demonstrate this argument. In particular, let H be the Hamiltonian of the spin-1 antiferromagnetic Heisenberg chain and U be the KT transformation, we prove that the self-dual model H + U H U is exactly equivalent to a gapless spin-1/2 XY chain, which also implies an emergent quantum anomaly. On the other hand, we show that the topological and trivial Ising criticalities that are dual to each other meet at a multicritical point which is indeed self-dual. Our discussions can be generalized to other symmetries beyond the spin-1 chains.

[1] T. Kennedy and H. Tasaki, Phys. Rev. B 45 (1992)
[2] M. Oshikawa, J. Phys. Condens. Matter 4 (1992)
[3] D. V. Else, S. D. Bartlett, and A. C. Doherty, Phys. Rev. B 88 (2013)
[4] H. Yang, L. Li, K. Okunishi, and H. Katsura, arXiv:2203.15791

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