PIRSA:23040155

The Higher Berry Phase and Matrix Product States

Ohyama, S. (2023). The Higher Berry Phase and Matrix Product States. Perimeter Institute. https://pirsa.org/23040155

Ohyama, Shuhei. The Higher Berry Phase and Matrix Product States. Perimeter Institute, Apr. 25, 2023, https://pirsa.org/23040155 

          @misc{ pirsa_PIRSA:23040155,
            doi = {10.48660/23040155},
            url = {https://pirsa.org/23040155},
            author = {Ohyama, Shuhei},
            keywords = {Condensed Matter},
            language = {en},
            title = {The Higher Berry Phase and Matrix Product States},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {apr},
            note = {PIRSA:23040155 see, \url{https://pirsa.org}}
          }

Shuhei Ohyama Kyoto University

DOI 10.48660/23040155
Collection
Talk Type Scientific Series
Subject

Abstract

The Berry phase, discovered by M.V. Berry in 1984, has been applied to the construction of various invariants in topological phase of matters. The Berry phase measures the non-triviality of a uniquely gapped system as a family and takes its value in $H^2({parameter space};Z)$.

In recent years, there have been several attempts to generalize it to higher-dimensional many-body lattice systems[1,2,3,4], called the “higher” Berry phase. In the case of spatial dimension d it is believed that the higher Berry phase takes its value in $H^{d+2}({parameter space};Z)$. However, in general dimensions, the definition of the higher Berry phase in lattice systems is not yet known.

In my talk, I’ll explain about the way to extract the higher Berry phase in 1-dimensional systems by using the “higher inner product” of three matrix product states and how to construct the topological invariant which takes its value in $H^3({parameter space};Z)$. This talk is based on [3] and [4].

Refs:
[1] A. Kapustin and L. Spodyneiko Phys. Rev. B 101, 235130
[2] X. Wen, M. Qi, A. Beaudry, J. Moreno, M. J. Pflaum, D. Spiegel, A. Vishwanath and M. Hermele arXiv:2112.07748
[3] S. Ohyama, Y. Terashima and  K. Shiozaki arXiv:2303.04252
[4] S. Ohyama and S. Ryu arXiv:2304.05356  

Zoom link:  https://pitp.zoom.us/j/93720709850?pwd=RTliMDNMRWo2V2k1MnBKUjlRMjBqZz09