Past Records of CREST Research Seminar on "Theoretical studies of topological phases of matter"

Speaker: Tomoki Ozawa (AIMR, Tohoku University)
Title: Topological band structure in quantum and classical systems
Date/Time: 16:00-17:30, Friday, November 27, 2020

Speaker: Nobuyuki Okuma (YITP, Kyoto University)
Title: Topology and anomaly in non-Hermitian skin effects: from index theorem to monopole catalysis
Date/Time: 16:00-17:30, Friday, December 4, 2020

Speaker: Yosuke Kubota (Shinshu University)
Title: Coarse geometry and operator algebra in condensed-matter physics
Date/Time: 16:00-17:30, Friday, January 8, 2021

Speaker: Yuan Yao (RIKEN)
Title: Critical parafermionic systems - from bosonization to parafermionization
Date/Time: 16:00-17:30, Friday, March 26, 2021
Abstract: In this talk, we will discuss a Zk parafermionization and bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from the conventional bosonization for k=2. The Zk parafermionization enables us to investigate the critical theories of parafermionic chains whose fundamental degrees of freedom are parafermionic, and we find that their modular covariance properties are unconventional in that their partition functions on a torus transform differently from any conformal field theory when k>2. Several concrete examples of lattice models will be discussed where parafermionic statistics can be manifested. This talk is based on the preprint: arxiv:2012.07529.

Speaker: Mayuko Yamashita (RIMS, Kyoto University)
Title: The classification problem of non-topological invertible QFT's and a physically motivated model for the Anderson duals
Date/Time: 16:00-17:30, Friday, April 23, 2021
Abstract: Freed and Hopkins conjectured that the deformation classes of non-topological invertible quantum field theories are classified by a generalized cohomology theory called the Anderson dual of bordism theories. The main difficulty of this problem lies in the fact that we do not have the axioms for QFT's. In this talk, I will explain the ongoing work to give a new approach to this conjecture. We construct a new, physically motivated model for the Anderson duals. This model is constructed so that it abstracts a certain property of invertible QFT's which physicists believe to hold in general. I will start from basic motivations for the classification problem, report the progress of our work and explain future directions. This is the joint work with Yosuke Morita (Kyoto, math) and Kazuya Yonekura (Kyushu, physics).

Speaker: Hosho Katsura (the University of Tokyo)
Title: The SU(N) Hubbard model: some rigorous results
Date/Time: 16:00-17:30, Friday, May 21, 2021

Speaker: Ryohei Kobayashi (ISSP, the University of Tokyo)
Title: Anomalies in (2+1)d fermionic topological phases and (3+1)d path integral state sums for fermionic SPT phases
Date/Time: 16:00-17:30, Friday, June 25, 2021

Speaker: Minkyu Kim (the University of Tokyo)
Title: Toric code induced by bicommutative Hopf algebras
Date/Time: 16:00-17:30, Friday, July 30, 2021

Speaker: Yoshimasa Hidaka (KEK)
Title: Higher group symmetry in axion electrodynamics
Date/Time: 16:00-17:30, Friday, September 17, 2021

Speaker: Shuhei Oyama (YITP, Kyoto University)
Title: Generalized Thouless Pump and the Matrix Product State (video)
Date/Time: 16:00-17:30, Friday, November 19, 2021

Speaker: Chris Bourne (Tohoku University)
Title: Fermionic gapped ground states and topological phases in the infinite volume limit
Date/Time: 16:00-17:30, Friday, December 17, 2021

Speaker: Kazuya Yonekura (Tohoku University)
Title: Classification of topologically nontrivial terms in action
Date/Time: 16:30-18:00, Friday, January 21, 2022

Speaker: Shingo Kobayashi (RIKEN)
Title: Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
Date/Time: 16:00-17:30, Friday, March 25, 2022

Speaker: Shin Hayashi (Tohoku University)
Title: Topological invariants related to corner states via index theory and matrix factorizations
Date/Time: 16:00-17:30, Friday, May 20, 2022

Speaker: Yuya Tanizaki (Yukawa Institute for Theoretical Physics, Kyoto University)
Title: Semiclassics with 't Hooft flux and confinement of 4d gauge theories via center vortices
Date/Time: 16:30-18:00, Friday, June 10, 2022
Abstract:Confinement of 4d gauge theories is usually the strong-coupling problem, and it is a difficult task to understand even its qualitative features. We are developing its semiclassical understanding based on the idea of volume independence or adiabatic continuity. We conjecture that the strong-coupling regime of many 4d gauge theories is continuously connected to the weak-coupling theories on small R2xT2 with the nontrivial ‘t Hooft flux. As a partial justification, we explicitly confirm that the dilute gas of center vortices can describe the fractional theta periodicity for pure YM theory and the chiral Lagrangian for QCD in this small T2 regime. We also uncover why this is possible in view of the 't Hooft anomaly matching condition.

Speaker: Kansei Inamura (ISSP, the University of Tokyo)
Title: Construction of 2d bosonic topological field theories with fusion category symmetries and their fermionization
Date/Time: 16:00-17:30, Friday, July 22, 2022

Speaker: Tsuneya Yoshida (University of Tsukuba)
Title: Effects of symmetry and interactions on exceptional points
Date/Time: 16:30-18:00, Friday, September 30, 2022

Speaker: Seishiro Ono (the University of Tokyo)
Title: High-throughput calculations of topological and nodal superconductivity in materials
Date/Time: 16:30-18:00, Friday, October 21, 2022
Abstract: Symmetry-transformation properties of Cooper pairs under spatial symmetries, dubbed pairing symmetry, are closely related to how electrons pair up. However, pairing symmetries for the majority of materials are not known. Sidestepping this issue, we tackle an alternative problem: we predict topological and nodal superconductivity in materials for each possible pairing symmetry. Our results could be compared with experimental results and reduce the candidates of pairing symmetries. In this talk, after reviewing our diagnostic scheme, we apply our method to some recently discovered superconductors. This talk is based on the following paper: Feng Tang*, Seishiro Ono*, Xiangang Wan, and Haruki Watanabe, Phys. Rev. Lett. 129, 027001 (2022).

Speaker: Yuji Hirono (Asia Pacific Center for Theoretical Physics)
Title: Structures and functions of chemical reaction networks
Date/Time: 16:00-17:30, Friday, November 25, 2022
Abstract: Chemical reactions form a large web of networks inside living cells and they are responsible for physiological functions. Understanding the behavior of complex reaction networks is a challenging and interesting problem. In this talk, I would like to illustrate how the techniques used in algebraic topology can shed light on the relationship between structures and functions of chemical reaction systems. In particular, we will discuss the following two problems: (1) response of reaction systems to external perturbations and (2) simplification of complex reaction networks without altering the behavior of the system.

Speaker: Ching-Kai Chiu (RIKEN)
Title: The connections between twisted bilayer physics and topological semimetals
Date/Time: 16:00-17:30, Friday, December 23, 2022

Speaker: Chris Bourne (Tohoku University)
Title: Index theory and topological phases for symmetric quantum walks
Date/Time: 16:00-17:30, Friday, January 20, 2023

Speaker: Masahiko G. Yamada (Gakushuin University)
Title: Matrix product renormalization group
Date/Time: 16:00-17:30, Friday, February 24, 2023

Speaker: Masaki Natori (the University of Tokyo)
Title: An alternative proof of Bott periodicity theorem using configuration spaces and bulk-edge correspondence
Date/Time: 16:00-17:30, Friday, May 26, 2023

Speaker: Yuto Moriwaki (RIKEN)
Title: Bootstrap hypothesis in two-dimension and the operad structure on moduli spaces
Date/Time: 16:00-17:30, Friday, June 9, 2023
Abstract: Conformal field theory is believed to be consistent (well-defined) if it satisfies the bootstrap equation. This claim is called the bootstrap hypothesis and is used, for example, in the numerical calculation of critical exponents for the 3-D Ising model. In this talk, we will formulate the bootstrap hypothesis mathematically in the two-dimensional case and give a proof under certain conditions. The consistency of 2d conformal field theory comes down to the representation theory of chiral conformal field theory (vertex operator algebra), and the important step in the proof is to show that the operad of the moduli spaces of punctured Riemann spheres acts topologically on the representation category of the vertex operator algebra. From this point of view, the bootstrap equation is a generator of a certain groupoid operad, and the consistency follows. This result is inspired by Huang-Kong's full field algebra, but we believe that our approach makes their result more conceptually comprehensible.

Speaker: Shoto Aoki (Osaka University)
Title: Curved domain-wall fermion and its anomaly inflow
Date/Time: 16:00-17:30, Friday, July 7, 2023

Speaker: Hiromi Ebisu (YITP, Kyoto University)
Title: 2+1d Foliated gauge theories and symmetry algebra
Date/Time: 16:30-18:00, Friday, September 8, 2023

Speaker: Mitsunobu Tsutaya (Kyushu University)
Title: Homotopy type of the space of finite propagation unitary operators on Z
Date/Time: 16:00-17:30, Friday, October 6, 2023

Speaker: Masataka Watanabe (Nagoya University)
Title: Physics of the Split Property
Date/Time: 16:00-17:30, Friday, November 10, 2023
Abstract: I will give a concrete physical procedure which obtains the intermediate Type I factor of von Neumann algebras of quantum field theories, used in defining the reduced density matrix and in computing the entanglement entropy.

Speaker: Philip Boyle Smith (Kavli IPMU)
Title: Duality webs of chiral fermionic CFTs with c ≤ 16
Date/Time: 17:00-18:30, Friday, December 22, 2023
Abstract: We classified all chiral fermionic CFTs of central charge ≤ 16 using Kac's theorem and bosonisation. This talk will discuss the derivation of this result, its application to non-supersymmetric heterotic strings, and how such theories fall into duality webs under topological manipulations involving the spin structure. The latter part will involve addressing some often-overlooked subtleties of bosonisation in gravitationally-anomalous theories, which we do from various perspectives involving anomalies, topological phases, and TFTs.

Speaker: Ryuichi Shindou (Peking University)
Title: Effect of weak band topology in metal-insulator transition in chiral symmetry classes
Date/Time: 16:30-18:00, Friday, February 9, 2024 (Note that the time slot is different from the usual one.)
Abstract: An interplay between disorder and a weak band topology in chiral symmetry classes leads to an intermediate phase between metal and Anderson localized phases, dubbed as "quasi-localized" phase, where wave function along a spatial direction with the weak topological index is delocalized but exponentially localized along the other direction(s). In this talk, I will introduce our recent studies on this topics.

Speaker: Motohiko Ezawa (the University of Tokyo)
Title: Topological-universal hybrid quantum computation based on Majorana fermions
Date/Time: 16:00-17:30, Friday, April 5, 2024
Abstract: We start with reviews on quantum computation and braiding of Majorana fermions. Then, we show that only the braiding of Majorana fermions is not enough for universal quantum computation due to the embedding problem, where certain gates including the CNOT gate cannot be embedded in larger qubits. This problem is solved by introducing many-body Majorana operators [1]. We also derive analytic formula for short Kitaev chain describing low-energy theory [2], which will be useful for recent experimental realization of Majorana fermions in quantum dots [3]. Finally, we show that an N-connected honeycomb chain of the Kitaev spin liquid model acts as 3N+2 qubits [4] and discuss how to braid and execute fusion based on local spin correlation operators.
[1] M. Ezawa, Systematic construction of topological-nontopological hybrid universal quantum gates based on many-body Majorana fermion interactions arXiv:2304.06260
[2] M. Ezawa, Robustness of Majorana edge states of short-length Kitaev chains coupled with environment, arXiv:2310.18083
[3] Tom Dvir, et. al. Realization of a minimal Kitaev chain in coupled quantum dots, Nature 614, 445 (2023).
[4] M. Ezawa, Braiding and fusion of Majorana fermions in minimal Kitaev spin liquid on a single hexagon with 5 qubits, arXiv:2401.01051

Speaker: Tetsuo Deguchi (Ochanomizu University)
Title: Exact results on the elasticity of polymer networks derived through homology in topology
Date/Time: 16:00-17:30, Friday, May 24, 2024
Abstract: The elastic theory of polymer networks such as phantom networks is reformulated and generalized in terms of homology in topology, so that useful exact results are derived not only for the Gaussian networks but also for polymer networks of chains with nonlinear potentials. For an illustration, the fractional power scaling behavior is shown in the chain-density dependence of the elastic modulus for polymer networks in melts, by making use of the results of phantom networks. Furthermore, a systematic method is presented for exactly calculating the nonlinear elasticity of such polymer networks that consist of finitely extensible ideal chains. It leads to an exact expression of the nonlinear elastic stress for any given lattice-type network. It is emphasized that spontaneous symmetry breaking plays a significant role in the elasticity of polymer networks, although it is usually not mentioned explicitly. Some of the derived results seem to be consistent with molecular dynamical simulations, scattering experiments and stress measurement of gels. In the introduction of this talk the standard theory of phantom networks is briefly reviewed and its potential difficulties are argued. The present talk is based on research results of the JST CREST project (2019 JPMJCR19T4) with the title: "Construction of homological topology theory on the elasticity of polymer networks and creation of devices through mixing ring polymers in polymeric materials" and in collaboration with Jason Cantarella, Clayton Shonkwiler and Erica Uehara.

Speaker: Kan Kitamura (RIKEN iTHEMS)
Title: Quantum symmetries on simple C*-algebras
Date/Time: 16:00-17:30, Friday, June 21, 2024

Speaker: Urei Miura (YITP, Kyoto University)
Title: Interacting Kitaev chain with \mathcal{N}=1 supersymmetry
Date/Time: 16:00-17:30, Friday, September 20, 2024

Speaker: Manato Fujimoto (Harvard University)
Title: Higher vortexability: zero field realization of higher Landau levels
Date/Time: 10:00-11:30, Friday, October 25, 2024

Speaker: Satoshi Yamaguchi (Osaka University)
Title: Noninvertible symmetries and boundaries in 3+1 dimensions
Date/Time: 16:00-17:30, Friday, November 29, 2024

Speaker: Mayuko Yamashita (Kyoto University)
Title: Topological elliptic genera
Date/Time: 16:30-18:00, Friday, December 20, 2024
Abstract: There is a classical construction of elliptic genera for SU-manifolds, which assigns Jacobi forms to SU-manifolds, and physically related to non-chiral 2d N=(2, 2) sigma models. In this talk, I explain my work with Ying-Hsuan Lin (arXiv:2412.02298) to give homotopy-theoretical refinements to it, which we call "topological elliptic genera". The codomain becomes the spectrum (in homotopy theoretical sense) called "Topological Jacobi Forms". I explain the construction and physical idea behind, and discuss a mathematical application where we derive an interesting divisibility result of Euler numbers.

Speaker: Mao Hoshino (University of Tokyo)
Title: A categorical perspective of non-formal equivariant quantizations
Date/Time: 16:00-17:30, Friday, February 21, 2025

Speaker: Yosuke Kubota (Kyoto University)
Title: Stable homotopy theory of invertible gapped quantum spin systems
Date/Time: 16:00-17:30, Friday, April 4, 2025
Abstract: In the past decade, A. Kitaev proposed that the set of invertible gapped quantum spin systems would form an \Omega-spectrum. This conjecture has potentially significant application to the study of SPT phases. We give a mathematically rigorous realization of this proposal with the language of functional analysis and operator algebra. Furthermore, we formulate the idea of placing a quantum spin system on a general space beyond R^n, which gives rise to a model of the generalized homology theory associated with Kitaev's spectrum. As an application, we study the topological phase of invertible phases protected by a crystallographic symmetry. This talk is based on the preprint arxiv:2503.12618.

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