Spontaneous Parity Violation in a Quantum Spin Chain

We report on a spontaneous breakdown of parity in the ground state of a spin Hamiltonian involving nearest-neighbor interactions. This occurs for a one-dimensional model where spins transform under the gauge field representation of QCD, the eight-dimensional adjoint representation of SU(3). The ground state spontaneously violates parity and is two-fold degenerate. In addition, the model possesses a non-vanishing topological string order parameter which we explicate analytically.