Kavli Affiliate: Yi Zhou
| First 5 Authors: Pei-Yuan Cai, Hui-Ke Jin, Yi Zhou, ,
| Summary:
We present a comprehensive study of topological phases in the SO($n$) spin
chains using a combination of analytical parton construction and numerical
techniques. For even $n=2l$, we identify a novel SPT$^2$ phase characterized by
two distinct topological sectors, exhibiting exact degeneracy at the matrix
product state (MPS) exactly solvable point. Through Gutzwiller-projected
mean-field theory and density matrix renormalization group (DMRG) calculations,
we demonstrate that these sectors remain topologically degenerate throughout
the SPT$^2$ phase, with energy gaps decaying exponentially with system size.
For odd $n=2l+1$, we show that the ground state remains unique. We precisely
characterize critical states using entanglement entropy scaling, confirming the
central charges predicted by conformal field theories. Our results reveal
fundamental differences between even and odd $n$ cases, provide numerical
verification of topological protection, and establish reliable methods for
studying high-symmetry quantum systems. The Gutzwiller-guided DMRG is
demonstrated to be notably efficient in targeting specific topological sectors.
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