论文标题
二元性，批判性，异常和拓扑1链中
Duality, Criticality, Anomaly, and Topology in Quantum Spin-1 Chains
论文作者
论文摘要
In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation $U_{\text{KT}}$, which defines a duality between the Haldane phase and the $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-breaking phase.在本文中，我们发现$ u _ {\ text {kt}} $还定义了拓扑结构阶段与微不足道的ising关键阶段之间的双重性，该阶段为拓扑关键性提供了“隐藏的对称性破坏”解释。此外，由于二元性与物质的不同阶段相关，因此我们认为具有自偶性的模型（即在$ u _ {\ text {kt}} $下不变的模型）很自然是至关重要的或多政治点。我们研究具体示例以证明这一论点。 In particular, when $H$ is the Hamiltonian of the spin-1 antiferromagnetic Heisenberg chain, we prove that the self-dual model $H + U_{\text{KT}} H U_{\text{KT}}$ is exactly equivalent to a gapless spin-$1/2$ XY chain, which also implies an emergent quantum anomaly.另一方面，我们表明，彼此双重的拓扑和微不足道的关键在多政治点相遇，这确实是自我划的。
In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation $U_{\text{KT}}$, which defines a duality between the Haldane phase and the $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry-breaking phase. In this paper, we find that $U_{\text{KT}}$ also defines a duality between a topological Ising critical phase and a trivial Ising critical phase, which provides a "hidden symmetry breaking" interpretation for the topological criticality. Moreover, since the duality relates different phases of matter, we argue that a model with self-duality (i.e., invariant under $U_{\text{KT}}$) is natural to be at a critical or multicritical point. We study concrete examples to demonstrate this argument. In particular, when $H$ is the Hamiltonian of the spin-1 antiferromagnetic Heisenberg chain, we prove that the self-dual model $H + U_{\text{KT}} H U_{\text{KT}}$ is exactly equivalent to a gapless spin-$1/2$ XY chain, which also implies an emergent quantum anomaly. On the other hand, we show that the topological and trivial Ising criticalities that are dual to each other meet at a multicritical point which is indeed self-dual.
