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arXiv · 1508.00960

Z_N Berry phase and symmetry protected topological phases of SU(N) antiferromagnetic Heisenberg chain

Yuichi Motoyama·Synge Todo
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Abstract

The local Z_N quantized Berry phase for the SU(N) antiferromagnetic Heisenberg spin model is formulated. This quantity, which is a generalization of the local Z_2 Berry phase for SU(2) symmetry, has a direct correspondence to the number of singlet pairs spanning on a particular bond, and is effective as a tool to characterize and classify the various symmetry protected topological phases of one-dimensional SU(N) spin systems. We extend the path-integral quantum Monte Carlo method for the Z_2 Berry phase in order to calculate the ZN Berry phase numerically. We demonstrate our method by calculating the Z_4 Berry phase for the bond-alternating SU(4) antiferromagnetic Heisenberg chain, which is represented by the Young diagram of four columns.

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Yuichi Motoyama, Synge Todo. 2015-08-05. Z_N Berry phase and symmetry protected topological phases of SU(N) antiferromagnetic Heisenberg chain. https://doi.org/10.1103/physrevb.98.195127

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