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MATSUI TAKU Last modified date:2023.04.10

Professor / mathematics
Faculty of Mathematics

Graduate School
Undergraduate School

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Academic Degree
Country of degree conferring institution (Overseas)
Field of Specialization
mathematical physics
Total Priod of education and research career in the foreign country
Outline Activities
We study structure of infinite volume ground states , limit theorem(central limit theorem)
of quantum spin systems by use of functional analysis. We initiated a mathematical study of uniqueness of equilibrium stets of anharmonic crystals.
Research Interests
  • analysis of statistical mechanics of quantum spin systems by functional analytic methods
    keyword : quantum spin sysytems, functional analysis,NESS, 高次元スピン系のHaag daulity Gemetric Interpretation of Z_2
    2009.04~2021.03* Spectral properties and symmetry breaking of Quantum systems  with infinite degree of freedom.
Current and Past Project
  • We analyse the type of various von Neumann sub-algebras appearing in GNS reprepresentations of gapped ground states of 2 dim quantum spin systems.
  • We study KMS and ground states of Bosonic systems on lattices using the resolevent algebras
    and we are trying to prove their uniqueness under physical natural situations.
  • We consider a generalization of Projected Entnagled Pair states and their symmetry.
  • We try to prove Haag duality for quatum systems on lattices in various situtations and
    we try to show that the presence of the spectral gap implies split property for one-dimensional systems.
    We als try to prove relative Haag duality (duality for relative commutants) and consider application to
    non-equilibrium steady states
  • In one-dimensional quantum spin systems, try to find a condition
    for producing infinitely many maximally entangled pairs of q-bits
    in pure states and investigate the relationship with split property.
  • * proof of absence of non-periodic ground states
     for anithferromagnetic XXZ models
    * clarify the relation between random partition and Bose-Einstein
Academic Activities
1. Taku Matsui Tomohiro Kanda, Regular KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra, 251-270, Analysis and Operator Theory(springer)に掲載, 2019.03, We proved existence and uniquness of KMS states for Weakly Coupled Anharmonic Crystals.
2. Keyl, M.; Matsui, T.; Schlingemann, D.; Werner, R. F. , Entanglement Haag-duality and type properties of infinite quantum spin chains.
, Rev. Math. Phys. , 18巻 9号 935--970.
, 2006.10.
3. Taku Matsu, Spectral gap, and split property in quantum spin chains,” J. Math. Phys. 51, 015216 (2010)JMAPAQ000051000001015216000001. | , Journal of Mathematical Physics, 51, 015216 (2010), 2010.01.
4. Taku Matsui, Boundedness of Entanglement Entropy and the Split property in Quantum Spin Chains
, MIレクチャーノート vol30 Mathematical Quantum Field Theory and Renormalization Theory , ISSN 1881-4042, 2011.01.
5. Taku Matsui, S.Yamagami, Kakutani dichotomy of free sates, Lett.Math.Phys., 102巻, 2012.08.
1. On Matrix product State of Quantum Spin Chain.
Membership in Academic Society
  • international association of mathemtatical physics
Educational Activities
Lectures on linear algebra, mathematical physics and
functional analysis