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

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.

6 pages, 2 figures

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Cited by in corpus (8)

• Higher-order topological phases in a spring-mass model on a breathing kagome lattice
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets
• Robust analytic continuation combining the advantages of the sparse modeling approach and Padé approximation
• DSQSS: Discrete Space Quantum Systems Solver
• Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S>1$): Quantized Berry phase and valence-bond solids
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Exact quantization of topological order parameter in SU($N$) spin models, $N$-ality transformation and ingappabilities