1. |
Taku Matsui, Tomohiro Kanda (学生１ 学生以外１）, Regular KMS states of weakly coupled anharmonic crystals and the resolvent CCR algebra. , * Analysis and operator theory, Springer Optim. Appl., 146, Springer, Cham, 2019. *, 146, 251-270, 2019.03, We consider equilibrium states of weakly coupled anharmonic quantum oscillators(= anharmonic crystal) on an integer lattice Z. We employed standard functional analytic methods for Schrödinger operators and we show existence of the infinite volume limit of equilibrium states, and uniqueness of the regular KMS (Kubo-Martin-Schwinger) states in the frame of Resolvent CCR Algebra introduced by D. Buchholz and H. Grundling.'' . |

2. |
Huzihiro Araki, Taku Matsui, Ground states of the XY-model, *Communications in Mathematical Physics*, 10.1007/BF01218760, 101, 2, 213-245, 1985.06, Ground states of the X Y-model on infinite one-dimensional lattice, specified by the Hamiltonian {Mathematical expression} with real parameters J≠0, γ and λ, are all determined. The model has a unique ground state for |λ|≧1, as well as for γ=0, |λ|<1; it has two pure ground states (with a broken symmetry relative to the 180° rotation of all spins around the z-axis) for |λ|<1, γ≠0, except for the known Ising case of λ=0, |λ|=1, for which there are two additional irreducible representations (soliton sectors) with infinitely many vectors giving rise to ground states. The ergodic property of ground states under the time evolution is proved for the uniqueness region of parameters, while it is shown to fail (even if the pure ground states are considered) in the case of non-uniqueness region of parameters.. |

3. |
Huzihiro Araki, Taku Matsui, Analyticity of ground states of the XY-model, *Letters in Mathematical Physics*, 10.1007/BF00417469, 11, 1, 87-94, 1986.01, Ground states of the XY-model obtained earlier are shown to depend analytically on parameters (λ, γ) of the model except at critical lines.. |

4. |
T. Matsui, On the implementability of non*Bogoliubov automorphisms of CAR algebras on fock spaces, *Letters in Mathematical Physics*, 10.1007/BF00402146, 14, 4, 363-369, 1987.11, We give necessary and sufficient conditions for the implementability of non^{*}Bogoliubov automorphisms of CAR algebras on Fock spaces. As an application, we show that certain (projective) representations of loop groups cannot be extended to bounded representations of their complexified groups.. |

5. |
Taku Matsui, The index of scattering operators of Dirac equations, *Communications in Mathematical Physics*, 10.1007/BF01205548, 110, 4, 553-571, 1987.12, A new index formula of Atiyah Singer type for scattering operators is proved. The index corresponds to the vacuum polarization of the Fermion (on the Minkowski space) coupled to an external non abelian gauge field.. |

6. |
T. Matsui, Uniqueness of the translationally invariant ground state in quantum spin systems, *Communications in Mathematical Physics*, 10.1007/BF02125695, 126, 3, 453-467, 1990.01, We introduce a class of quantum spin systems on ℤ^{d}. We show that the translationally invariant ground state is unique for this system if it is in a strong external field.. |

7. |
T. Matsui, The index of scattering operators of Dirac equations, II, *Journal of Functional Analysis*, 10.1016/0022-1236(90)90029-K, 94, 1, 93-109, 1990.01, The index formula of scattering operators of the previous paper of the author (T. Matsui, The index of scattering operators of Dirac equations, Commun. Math. Phys.110 (1987) 553-571) is shown to hold for a wider class of potentials which contains both gauge potentials with compactly supported energy and instantontype potentials.. |

8. |
Taku Matsui, A link between quantum and classical Potts models, *Journal of Statistical Physics*, 10.1007/BF01025850, 59, 3-4, 781-798, 1990.05, We study ground states of quantum Potts models. We construct ground states of certain d-dimensional quantum models as Gibbs measures of a d-dimensional classical spin system. Our results imply that various phenomena of classical spin systems can also be found in quantum ground states.. |

9. |
T. Matsui, Gibbs measure as quantum ground states, *Communications in Mathematical Physics*, 10.1007/BF02097657, 135, 1, 79-89, 1990.12, We study certain quantum spin systems which are equivalent to stochastic Ising models. We show that any translationally invariant quantum ground state is given by integration of Gibbs measure. The existence of mass gap is shown to be the same as exponentially fast convergence of stochastic models to invariant states.. |

10. |
Taku Matsui, On Ground State Degeneracy of Z_{2} Symmetric Quantum Spin Models, *Publications of the Research Institute for Mathematical Sciences*, 10.2977/prims/1195169424, 27, 4, 657-679, 1991.01, We consider a class of Z_{2} symmetric quantum spin Hamiltonians. Anisotropic spin 1/2 Heisenberg models are typical examples. Proof of groound state degeneracy (Z_{2} symmetry breaking), construction of pure gournd states are given in a systematic way.. |

11. |
Taku Matsui, Remarks on duality of 1 dimensional quantum spin models, *Communications in Mathematical Physics*, 10.1007/BF02096566, 150, 1, 65-81, 1992.11, We present some results on duality maps and ground states of 1 dimensional quantum spin models. We also give some applications to Kramers Wannier duality and the nonlocal transformation that Kennedy and Tasaki discovered in their study of Haldane phase of quantum antiferromagnetic spin models.. |

12. |
Taku Matsui, Markov semigroups which describe the time evolution of some higher spin quantum models, *Journal of Functional Analysis*, 10.1006/jfan.1993.1109, 116, 1, 179-198, 1993.08, We consider perturbation of spin’s ferromagnetic Heisenberg models in infinite volume ground state representations. Imaginary time evolution gives rise to a Markov semigroup on a configuration space of the classical spin system. We establish a correspondence of reversible measures for Markov semigroups and ground states of quantum systems on the same dimensional lattice.. |

13. |
Taku Matsui, Purification and uniqueness of quantum Gibbs states, *Communications in Mathematical Physics*, 10.1007/BF02102020, 162, 2, 321-332, 1994.05, We give a new condition for uniqueness of Gibbs states of quantum spin models on lattices.. |

14. |
Taku Matsui, On Ground States of the One-Dimensional Ferromagnetic XXZ Model, *Letters in Mathematical Physics*, 37, 4, 397-403, 1996.01, We obtain the complete list of pure infinite volume ground states for the one-dimensional ferromagnetic XXZ model.. |

15. |
Taku Matsui, Ground states of Fermions on lattices, *Communications in Mathematical Physics*, 10.1007/BF02506423, 182, 3, 723-751, 1996.01, We consider Fermion systems on integer lattices. We establish the existence of dynamics for a class of long range interactions. The infinite volume ground states are considered. The equivalence of the variational principle and ground state conditions is proved for long range interactions. We also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full CAR algebra for the Hamiltonian with a chemical potential (equivalence of ensemble for canonical and ground canonical states at the zero temperature).. |

16. |
Taku Matsui, Translational symmetry breaking and soliton sectors for massive quantum spin models in 1 + 1 dimensions, *Communications in Mathematical Physics*, 10.1007/s002200050193, 189, 1, 127-144, 1997.01, We consider the classification of pure infinite volume ground states and that of soliton sectors for 1+1 dimensional massive quantum spin models. We obtain a proof that non-translationally invariant ground state cannot exist for a class of translationally invariant Hamiltonians including the spin 1 AKLT (Affleck Kennedy Lieb Tasaki) antiferromagnetic spin model. We also obtain a complete classification of soliton sectors (up to unitary equivalence) for certain massive models (e.g. ferromagnetic XXZ models).. |

17. |
Taku Matsui, On the Spectra of the Kink for Ferromagnetic XXZ Models, *Letters in Mathematical Physics*, 10.1023/A:1007396827804, 42, 3, 229-239, 1997.01, We consider the kink (infinite volume nontranslationally invariant ground states) of the ferromagnetic XXZ models on the multi-dimensional lattices. We obtained the following results: (i) The pure states satisfying the local zero energy condition are necessarily product states, (ii) The Hamiltonian in the GNS representation of the kink has no gap between the ground-state eigenvalue and the rest of the spectra.. |

18. |
Taku Matsui, A characterization of pure finitely correlated states, *Infinite Dimensional Analysis, Quantum Probability and Related Topics*, 10.1142/S0219025798000351, 1, 4, 647-661, 1998.01, We give a characterization of pure finitely correlated states (quantum Markov states) as zero energy states of UHF algebras.. |

19. |
Taku Matsui, Bosonic central limit theorem for the one-dimensional XY model, *Reviews in Mathematical Physics*, 10.1142/s0129055x02001272, 14, 7-8, 675-700, 2002, We prove the central limit theorem for Gibbs states and ground states of quasifree Fermions (bilinear Hamiltonians) and those of the off critical XY model on a one-dimensional integer lattice.. |

20. |
Detlev Buchholz, Masaki Izumi, Taku Matsui, Reviews in Mathematical Physics Editorial, *Reviews in Mathematical Physics*, 14, 7-8, 2002.07. |

21. |
S. Tasaki, T. Matsui, Nonequilibrium steady states with Bose-Einstein condensates, *Stochastic Analysis
Classical and Quantum: Perspectives of White Noise Theory*, 10.1142/9789812701541_0017, 211-227, 2005.01, Nonequilibrium steady states (NESS) of bosonic system with Bose-Einstein condensate are investigated with the aid of the C*-gebraic method. The system consists of two free bosonic reservoirs coupled with each other. Initially the reservoirs are prepared to be in equilibrium with different temperatures and local densities. NESS are constructed as the t → +∞ limits of such initial states. Josephsoncurrents are studied as well.. |

22. |
Taku Matsui, BEC of free bosons on networks, *Infinite Dimensional Analysis, Quantum Probability and Related Topics*, 10.1142/S0219025706002202, 9, 1, 1-26, 2006.03, We consider free bosons hopping on a network (infinite graph). The condition for Bose-Einstein condensation is given in terms of the random walk on a graph. In case of periodic lattices, we also consider boson moving in an external periodic potential and obatin the criterion for Bose-Einstein condensation.. |

23. |
M. Keyl, T. Matsui, D. Schlingemann, R. F. Werner, Entanglement, haag-duality and type properties of infinite quantum spin chains, *Reviews in Mathematical Physics*, 10.1142/S0129055X0600284X, 18, 9, 935-970, 2006.10, We consider an infinite spin chain as a bipartite system consisting of the left and right half-chains and analyze entanglement properties of pure states with respect to this splitting. In this context, we show that the amount of entanglement contained in a given state is deeply related to the von Neumann type of the observable algebras associated to the half-chains. Only the type I case belongs to the usual entanglement theory which deals with density operators on tensor product Hilbert spaces, and only in this situation separable normal states exist. In all other cases, the corresponding state is infinitely entangled in the sense that one copy of the system in such a state is sufficient to distill an infinite amount of maximally entangled qubit pairs. We apply this results to the critical XY model and show that its unique ground state φs provides a particular example for this type of entanglement.. |

24. |
M. Keyl, Taku Matsui, D. Schlingemann, R. F. Werner, On haag duality for pure states of quantum spin chains, *Reviews in Mathematical Physics*, 10.1142/S0129055X08003377, 20, 6, 707-724, 2008.07, In this note, we consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semi-infinite intervals (-∞ , 0] and [1, ∞) when the von Neumann algebra generated by observables localized in [0, ∞) is non-type I.. |

25. |
Tomohiro Kanda, Taku Matsui, Regular KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra, *Springer Optimization and Its Applications*, 10.1007/978-3-030-12661-2_12, 251-270, 2019, We consider equilibrium states of weakly coupled anharmonic quantum oscillators(= anharmonic crystal) on an integer lattice Z. We employed standard functional analytic methods for Schrödinger operators and we show existence of the infinite volume limit of equilibrium states, and uniqueness of the regular KMS (Kubo–Martin–Schwinger) states in the frame of Resolvent CCR Algebra introduced by D. Buchholz and H. Grundling.. |

26. |
Taku Matsui, Spectral gap, and split property in quantum spin chains, *Journal of Mathematical Physics*, 10.1063/1.3285046, 51, 1, 2010.01, In this article, we consider a class of ground states with spectral gap for quantum spin chains on an integer lattice and we prove that the factorization lemma of Hastings ["Topology and phases in fermionic systems," J. Stat. Mech.: Theory Exp.2008, L01001] implies split property (weak statistical independence) of left and right semi-infinite subsystems.. |

27. |
Taku Matsui, Shigeru Yamagami, Kakutani Dichotomy on Free States, *Letters in Mathematical Physics*, 10.1007/s11005-012-0579-0, 102, 3, 285-295, 2012.10, Two quasi-free states on a CAR or CCR algebra are shown to generate quasi-equivalent representations unless they are disjoint.. |

28. |
Taku Matsui, Boundedness of entanglement entropy and split property of quantum spin chains, *Reviews in Mathematical Physics*, 10.1142/S0129055X13500177, 25, 9, 2013.10, We show that boundedness of entanglement entropy for pure states of bipartite quantum spin systems implies split property of subsystems. As a corollary, in one-dimensional quantum spin chains, we show that the split property with respect to left and right semi-infinite subsystems is valid for the translationally invariant pure ground states with spectral gap.. |

29. |
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. |

30. |
T.Matsui, BEC of Free Bosons on Networks, *Infinite dimensional analysis, quantum probabilitiy and related topics*, Vol.9 Number1 1-26, 2006.03. |

31. |
T.Matsui, On the absence of non-periodic ground states for the antiferromagnetic XXZ model., *Commun.Math.Phys.*, 10.1007/s00220-004-1236-y, 253, 3, 585-609, 253, p585-609, 2005.01. |

32. |
Y. Shimada, T.Matsui, On quasifree representations of infinite dimensional symplectic group, *J. Funct. Anal.*, 10.1016/j.jfa.2004.01.005, 215, 1, 67-102, 215 p67--102., 2004.01. |

33. |
S. Tasaki, T.Matsui, Fluctuation theorem, nonequilibrium steady states and MacLennan-Zubarev ensembles of a class of large quantum systems., *Quantum Prob. White Noise Anal.*, 17 p100--119, 2003.01. |

34. |
Y.Ogata,T.Mtsui, Variational principle for non-equilibrium steady states of the XX model, *Rev. Math. Phys.*, 10.1142/S0129055X03001850, 15, 8, 905-923, 15 p905-923, 2003.01. |

35. |
T.Matsui, On the algebra of fluctuation in quantum spin chains., *Ann. Henri Poincare*, 10.1007/s00023-003-0122-z, 4, 1, 63-83, 4 p 63-83, 2003.01. |

36. |
T.Matsui, On Non-Commutative Ruelle Transfer Operator, *Rev.Math.Phys.*, 10.1142/S0129055X01001034, 13, 10, 1183-1201, Vol.13, p1183-1201, 2001.01. |

37. |
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. |

38. |
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. |

39. |
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. |

40. |
Taku Matsui, S.Yamagami, Kakutani dichotomy of free sates, *Lett.Math.Phys.*, １０２巻, 2012.08. |