Dimerization in Quantum Spin Chains with O(n) Symmetry

We consider quantum spins with S >= 1, and two-body interactions with O (2S + 1) symmetry. We discuss the ground state phase diagram of the one-dimensional system. We give a rigorous proof of dimerization for an open region of the phase diagram, for S sufficiently large. We also prove the existence of a gap for excitations.

Automated summary

The study focuses on quantum spins with S ≥ 1 and two-body interactions with O (2S + 1) symmetry in a one-dimensional system. A rigorous proof of dimerization within an open region of the phase diagram for sufficiently large S is presented, along with the proof of the existence of a gap for excitations.