Talk by Shuhei Ohyama (Kyoto University)

Higher structures in matrix product states

Time & Date: Monday, 16 October 2023, 11:30

Location: Kurt Gödel lecture room (room 3E63 on the ground floor of the Faculty of Physics, Strudlhofgasse 4, 1090 Vienna)

Abstract: The Berry phase, introduced by Michael V. Berry in 1984, has been widely applied in the definition of topological invariants, inspired by the trend of topological phases originating from quantum Hall systems. However, when naively calculating the Berry phase for high-dimensional many-body Hamiltonians, a divergence problem arises in the thermodynamic limit, necessitating an appropriate generalization of the definition of the Berry phase. In this seminar, I will discuss the formulation of higher Berry phases in one-dimensional systems, based on [1-3]. Specifically, by employing the matrix product state, we define the inner product for three states and demonstrate how this quantity provides a natural definition of the higher Berry phase. Please refer to similar studies from other groups as well [4,5].

[1] Shuhei Ohyama, Yuji Terashima, Ken Shiozaki arXiv:2303.04252.
[2] Shuhei Ohyama, Shinsei Ryu arXiv:2304.05356.
[3] Ken Shiozaki, Niclas Heinsdorf, Shuhei Ohyama, arXiv:2305.08109.
[4] Marvin Qi, David T. Stephen, Xueda Wen, Daniel Spiegel, Markus J. Pflaum, Agnès Beaudry, Michael Hermele arxiv:2305.07700.
[5] Daniel Spiegel, arXiv:2305.07951.

Host: Norbert Schuch