| 研究実績の概要 |
The concept of duality plays an important role in physics. For example, in quantum spin chains, the Kennedy-Tasaki (KT) duality provides an essential interpretation of the gapped topological phases. In this work, we find that the KT duality has a more significant impact than what has been known: the duality also provides a fundamental understanding of the gapless topological phases in quantum spin-1 chains. Surprisingly, these nontrivial findings can be demonstrated by celebrated models with rather elementary techniques. Considering that the gapless topological phases have been of particular interest recently, we believe our work will stimulate new research in this field.
In quantum spin-1 chains, it has been known that the Kennedy-Tasaki (KT) transformation defines a duality between the symmetry-protected topological (SPT) phase and the symmetry-breaking phase. In our work, we revisit the KT duality and reveal that the duality also works in gapless systems: The KT duality provides a “hidden symmetry breaking” interpretation for the topological criticality. In other words, the KT transformation relates a trivial Ising criticality and an SPT Ising criticality to each other. We demonstrate our arguments by constructing a (1+1)D model which is defined by interpolating between the spin-1 bilinear-biquadratic chain and its KT dual. We find that our model is exactly equivalent to a spin-1/2 XXZ chain at the self-dual point. Since the spin-1/2 XXZ model is exactly solvable, the low-energy theory at the self-dual point becomes clear.
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