The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped

Hal Tasaki

doi:10.1103/physrevlett.134.076602

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arXiv · 2407.17041

The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped

Hal Tasaki

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Abstract

Under the widely accepted but unproven assumption that the one-dimensional S=1 antiferromagnetic Heisenberg model has a unique gapped ground state, we prove that the model belongs to a nontrivial symmetry-protected topological (SPT) phase. In other words, we rigorously rule out the possibility that the model has a unique gapped ground state that is topologically trivial. To be precise, we assume that the models on open finite chains with boundary magnetic field have unique ground states with a uniform gap and prove that the ground state of the infinite chain has a nontrivial topological index. This further implies the presence of a gapless edge excitation in the model on the half-infinite chain and the existence of a topological phase transition in the model that interpolates between the Heisenberg chain and the trivial model.

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Hal Tasaki. 2024-07-24. The Ground State of the S=1 Antiferromagnetic Heisenberg Chain is Topologically Nontrivial if Gapped. https://doi.org/10.1103/physrevlett.134.076602

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