Duality, criticality, anomaly, and topology in quantum spin-1 chains

Article

关键词: ISOTROPIC HEISENBERG CHAIN;    BOND GROUND-STATES;    SYMMETRY-BREAKING;    SURFACE-ENERGY;    EXCITATIONS;    PHASES;    PART;    GAP;   

DOI  :  10.1103/PhysRevB.107.125158

来源: SCIE

【 摘 要 】

In quantum spin-1 chains, there is a nonlocal unitary transformation known as the Kennedy-Tasaki transformation U-KT, which defines a duality between the Haldane phase and the Z(2) X Z(2) symmetry-breaking phase. In this paper, we find that U-KT also defines a duality between a topological Ising critical phase and a trivial Ising critical phase, which provides a hidden symmetry breaking interpretation of 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-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 + UKTHUKT 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 critical phases that are dual to each other meet at a multicritical point which is indeed self-dual.

【 授权许可】

Free