Abstract Lieb-Schultz-Mattis (LSM) theorems impose non-perturbative constraints on the
zero-temperature phase diagrams of quantum lattice Hamiltonians (always assumed to be …

In this work, we study quantum many-body systems which are self-dual under duality
transformation connecting different symmetry protected topological (SPT) phases. We …

We present the Bilinear Phase Map (BPM), a concept that extends the Kramers-Wannier
(KW) transformation to investigate unconventional gapped phases, their dualities, and …

Spin parity effects refer to those special situations where a dichotomy in the physical
behavior of a system arises, solely depending on whether the relevant spin quantum …

We consider the quantum spin ice models in the planar pyrochlore lattice. The models are
obtained by perturbing the Ising model with different lattice symmetry preserving quantum …

This Dissertation studies two closely related topics: fermionic Lieb-Schultz-Mattis (LSM)
Theorems and invertible fermionic topological (IFT) phases of matter. The original LSM …