MATSUI, Chihiro

Associate Professor
Mathematical physics
Research interests
Quantum solvable models, Solvable stochastic processes
Current research

My main research interest is quantum solvable models. Although no clear definition is given for quantum solvable models, here we say a system is solvable when many-body scatterings are decomposed into a sequence of two-body scatterings. The decomposability of many-body scatterings into two-body ones is guaranteed by the Yang-Baxter equation. The Yang-Baxter equation is understood in the context of algebra such as quantum groups, and thus allows us to derive exact physical quantities through the algebraic relations. The famous example is the spin-1/2 Heisenberg chain with anisotropy called the XXZ chain. A Scattering process of a quantum field theory (QFT) is described by the transfer matrix of the corresponding spin chain. This is achieved by considering the discretization of the light cone, called the light-cone lattice regularization. The XXZ model is a non-supersymmetric model, while its extension to the higher-spin cases allows us to obtain the supersymmetry in their corresponding QFTs. The aim of my research is to explore how the supersymmetry arises in the corresponding QFTs to the non-supersymmetry spin chains from the viewpoint of characteristic degrees of freedom in the higher-spin cases. Another topic of my research interest is solvable stochastic processes. The asymmetric simple exclusion process (ASEP) is a one-dimensional stochastic process with discrete space and continuum time. This model obeys a master equation with a Markov matrix, which satisfies the Temperley-Lieb algebra, and thus leads to solvability of the system in the sense that the steady states are exactly derived. Due to the nice mathematical structure of the Markov matrix, various algebraic extensions of the ASEP can be considered. The multi-state extension, which allows more than one particle to occupy the same site, is achieved by considering the higher-dimensional representation of the Temperley-Lieb algebra. This model describes multiple particles hopping at the same time on one dimension and, therefore, is applicable to micromeritics and traffic engineering.

Selected publications
  1. T. Deguchi and C. Matsui, "Form factors of integrable higher-spin XXZ chains and the affine quantum-group symmetry", Nucl. Phys. B814, pp. 405-438 (2009).
  2. T. Deguchi and C. Matsui, "Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method", Nucl. Phys. B831, pp. 359-407 (2010).
  3. C. Matsui, "Boundary effects on the supersymmetric sine-Gordon model through light-cone approach", Nucl. Phys. B885, pp. 373-408 (2014).
  4. C. Matsui, "Multi-state asymmetric simple exclusion processes", J. Stat. Phys. 158, pp. 158-191 (2015).
  5. C. Arita and C. Matsui, "Phase coexistence phenomena in an extreme case of the misanthrope process with open boundaries", Europhys. Lett. 114, 60012 (2016).
  6. C. Matsui, "Spinon excitations in the spin-1 XXZ chain and hidden supersymmetry", Nucl. Phys. B913, pp. 15-33 (2016).

Memberships, activities and


The Physical Society of Japan

The Mathematical Society of Japan

2017- Journal editorial board of the membership journal of The Physical Society of Japan