6 problems

Let ${\cal H}$ be the Hamiltonian, $d$ the spatial dimension, $L$ the linear system size, and let $T$ be the twist operator. For inverse temperature $\beta$, define the thermal exp…

Let $L$ denote the linear system size, $V$ the volume, $d$ the spatial dimension, and $V/L$ the system width. Assume that the width $V/L$ is of order $L^{d-1}$ and that $d>1$. Even…

Let $G$ be the space group No. 227 and let the full symmetry be $\mathcal{G}=G\times\mathrm{SO}(3)$. Consider a symmetry-fractionalization pattern for an emergent $(3+1)$-dimension…

Let a crystallographic group $G$ act on a lattice, and let a symmetric short-range-entangled phase (sym-SRE phase) mean a phase preserving the symmetry and having no intrinsic long…

Lieb-Schultz-Mattis conjecture for projective symmetries. Such a quantum spin chain cannot have a symmetric gapped ground state in the thermodynamic limit.

Let a quantum spin chain have half-odd-integral spin. Assume that its interaction is short ranged and translation invariant, and that it possesses time-reversal symmetry or…