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Title: Symmetry Protected Topological Phases in Quantum Integer Spin Chains
Originating Office: IAS
Speaker: Zhang, Guang-Ming
Issue Date: 15-Dec-2012
Event Date: 15-Dec-2012
Group/Series/Folder: Record Group 8.15 - Institute for Advanced Study
Series 3 - Audio-visual Materials
Location: 8.15:3 box 1.8
Notes: IAS Asia Pacific Workshop on Condensed Matter Physics. Talk no. 18
Title from title slide.
Host: Institute for Advanced Study.
Sponsor: The Collaborative Research Fund (CRF), The Research Grants Council (RGC).
Abstract: Many years ago, from the theory of nonlinear sigma model with theta term, Haldane predicted that antiferromagnetic Heisenberg spin chains are classified into two universality classes: half-odd integer spins with gapless excitations and integer spins with gapped excitations. The Haldane gap phases can be regarded as an example of a symmetry protected topological (SPT) phase in 1D. For a quantum Heisenberg antiferromagnetic spin-1 chain, nonlocal string order parameters are proposed to describe the hidden antiferromagnetic correlations, and a unitary nonlocal transformation was established to convert the nonlocal string order parameters to the local ones and to reveal the hidden discrete Z2 x Z2 symmetry. Recently, we have developed a similar description scheme for the higher integer spin chains, where the required higher symmetry SO(2S+1) in the ground state is essential. Moreover, recent studies have indicated that the Haldane gapped phase with an odd integer spin is a SPT phase and the fractionalized edge spins are symmetry protected, while the even integer spin phase is not. In order to consider the question as whether the differences between the odd and even integer Haldane gapped phases can be understood from their effective field theories, we carefully examine the effective field theory of the Bethe ansatz integrable spin-S Heisenberg antiferromagnetic chains. It shows that the quantum critical theories for the integer spin chains should be characterized by the SO(3) level-S Wess-Zumino-Witten model. There exist two distinct universality classes determined by the parity of the integer spin number, and associated with two completely different conformal field theories. We further show that these two classes of critical states describe the boundary theory of a two-dimensional doubled Chern-Simons topological field theory on an SO(3) group manifold with spin structure.
Duration: 42 min.
Appears in Series:8.15:3 - Audio-visual Materials
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