Kavli Affiliate: Yi Zhou
| First 5 Authors: , , , ,
| 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 in close
chains 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 in close chains. 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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