The New Phases due to Symmetry Protected Piecewise Berry Phases

Hiromu Araki, Yasuhiro Hatsugai, Tomonari Mizoguchi

Robert Olkiewicz

Toshikaze Kariyado, Takahiro Morimoto, Yasuhiro Hatsugai

We show that the Z_{N} Berry phase (Berry phase quantized into 2π/N) provides a useful tool to characterize symmetry protected topological phases with correlation that can be directly computed through numerics of a relatively small system size. The Z_{N} Berry phase is defined in a N-1-dimensional parameter space of local gauge twists, which we call the "synthetic Brillouin zone," and an appropriate choice of an integration path consistent with the symmetry of the system ensures exact quantization of the Berry phase. We demonstrate the usefulness of the Z_{N} Berry phase by studying two 1D models of bosons, SU(3) and SU(4) Affleck-Kennedy-Lieb-Tasaki models, where topological phase transitions are captured by Z_{3} and Z_{4} Berry phases, respectively. We find that the exact quantization of the Z_{N} Berry phase at the topological transitions arises from a gapless band structure (e.g., Dirac cones or nodal lines) in the synthetic Brillouin zone.

Hiromu Araki, Tomonari Mizoguchi, Yasuhiro Hatsugai

The authors propose that the quantized Berry phase serves as a many-body topological invariant that characterizes the higher-order symmetry-protected topological phases in two- and three-dimensions, and provides a clear insight of bulk-corner correspondence. The quantized Berry phase has wide applicability ranging from fermionic models with and without interactions to spin models.

Lian-Ao Wu, Jing Sun, Ji-Yu Zhong

Stefan Giller, Cezary Gonera, Piotr Kosiński +1 more