SO(n) AKLT Chains as Symmetry Protected Topological Quantum Ground States

Understand

This thesis studies a pair of symmetry protected topological (SPT) phases which arise when considering one-dimensional quantum spin systems possessing a natural orthogonal group symmetry.

• Particular attention is given to a family of exactly solvable models whose ground states admit a matrix product state description and generalize the AKLT chain.
• We call these models ``$SO(n)$ AKLT chains'' and the phase they occupy the ``$SO(n)$ Haldane phase''.
• We present new results describing their ground state structure and, when $n$ is even, their peculiar $O(n)$-to-$SO(n)$ symmetry breaking.