Lowest-energy states in parity-transformation eigenspaces of SO(N) spin chain

TL;DR

This paper investigates the symmetry properties of SO(N) spin chains, revealing the structure of their lowest-energy states within parity eigenspaces and their degeneracies at specific points.

Contribution

It extends the symmetry analysis of SO(N) spin chains to include O(N) and characterizes the lowest-energy states in parity eigenspaces, showing their nondegeneracy and tensor structures.

Findings

Lowest-energy states are nondegenerate within parity eigenspaces.

States form antisymmetric tensors or pseudotensors.

Ground state degeneracy at the valence-bond solid point is 2^{N-1}.

Abstract

We expand the symmetry of the open finite-size SO(N) symmetric spin chain to O(N). We partition its space of states into the eigenspaces of the parity transformations in the flavor space, generating the subgroup $Z_2^{\times(N-1)}$. It is proven that the lowest-energy states in these eigenspaces are nondegenerate and assemble in antisymmetric tensors or pseudotensors. At the valence-bond solid point, they constitute the $2^{N-1}$-fold degenerate ground state with fully broken parity-transformation symmetry.