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

We have an online seminar on "Theoretical studies of topological phases of matter", which is a research subject in the CREST program "Creation of Core Technology based on the Topological Materials Science for Innovative Devices" of Japan Science and Technology Agency. This is supported by the CREST Grant (Number: JPMJCR19T2) held by Yasuyuki Kawahigashi (the University of Tokyo) together with Akira Furusaki (RIKEN) and Masatoshi Sato (Yukawa Institute for Theoretical Physics, Kyoto University). The aim of this seminar is to foster interactions between mathematicians and physicists and promote joint research among the CREST group members. We plan to have one talk every month approximately.

• Speaker: Kenji Shimomura (YITP, Kyoto University)
• Title: Nonequilibrium steady state in Lindblad dynamics for infinite quantum spin systems and nonnormality-induced spontaneous symmetry breaking
• Date/Time: 16:00-17:30, Friday, November 7, 2025
• Abstract: For open quantum systems obeying a Lindblad equation, it is a challenging problem to clarify and classify what kind of non-equilibrium steady state (NESS) the system relaxes to after a sufficiently long time. In this talk, we consider open quantum spin systems on infinite lattices described by the Lindblad equation and present a definition of the NESS in such infinite systems. The NESS in infinite systems is not necessarily equivalent to the thermodynamic limit of the NESS in finite systems; the former may correspond in finite systems to a metastable state, not a NESS. We see this in a solvable model. We also find a sufficient condition for equivalence of them, which relates to both the Liouvillian gap and nonnormality, i.e., nonorthogonality among eigenmodes of the Liouvillian. The enhancement of nonnormality can cause spontaneous symmetry breaking (SSB) for the NESS in infinite systems, which we dub nonnormality-induced SSB. Since a Liouvillian is normal in unitary dynamics, such a type of SSB is unique to open quantum systems. Furthermore, the nonnormality-induced SSB can occur even when the Liouvillian is gapped. This work uncovers a novel phase of matter in open quantum systems and establishes a way to classify it by focusing on nonnormality. This talk is based on the preprint arXiv:2508.07448.

Registration

The talk will be online with Zoom. The Zoom link will be sent by e-mail to those who have registered on the above form. If you have any inquiry, please contact Kawahigashi (yasuyuki@ms.u-tokyo.ac.jp).

Records of Past Seminars

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