Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states

TL;DR

This paper introduces a class of exactly solvable SO(n) symmetric spin chains with matrix product ground states, revealing distinct phases and hidden order parameters for odd and even n.

Contribution

The authors construct exactly solvable SO(n) symmetric Hamiltonians with novel ground states, including Haldane gap and dimerized phases, and analyze their hidden order and phase diagram.

Findings

For odd n, ground state is a Haldane gap spin liquid.

For even n, ground state is a twofold degenerate dimerized state.

Hidden antiferromagnetic order characterized by nonlocal string order parameters.

Abstract

We introduce a class of exactly solvable SO(n) symmetric Hamiltonians with matrix product ground states. For an odd $n\geq 3$ case, the ground state is a translational invariant Haldane gap spin liquid state; while for an even $n\geq 4$ case, the ground state is a spontaneously dimerized state with twofold degeneracy. In the matrix product ground states for both cases, we identify a hidden antiferromagnetic order, which is characterized by nonlocal string order parameters. The ground-state phase diagram of a generalized SO(n) symmetric bilinear-biquadratic model is discussed.