Novel Quantum Phases in Low Dimensions

We introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states. We prove that the ground state of our model is non-degenerate and exhibits a novel quantum phase transition from bounded entanglement entropy to a massively entangled state with volume entropy scaling. The ground state may be interpreted as a deformation away from the uniform superposition of colored Motzkin paths, shown by Movassagh and Shor, that has a large (square-root) but sub-extensive scaling of entanglement. We carry out the same procedure for both integer and half integer versions of the spin chain, and established upper bounds on the spectral gap for certain phases of the model.

Time reversal symmetric topological superconductors in three spatial dimensions carry gapless surface Majorana fermions. They are robust against any time reversal symmetric single-body perturbation weaker than the bulk energy gap. We mimic the massless surface Majorana's by coupled wire models in two spatial dimensions. We introduce explicit many-body inter-wire interactions that preserve time reversal symmetry and give energy gaps to all low energy degrees of freedom. We show the gapped models generically carry non-trivial topological order and support anyonic excitations.