: Lieb-Schultz-Mattis (LSM) theorem is a famous example of universality in a quantum many-body system, where its symmetry and filling constrain the nature of all possible ground states, irrespective of the specific form of the Hamiltonian. In this talk I will discuss a family of generalized LSM theorems, which forces any short-range-entangled ground state to be a topological insulator, or more generally a symmetry protected topological (SPT) phase. We call such a system a LSM-SPT system. I will discuss how to construct a LSM-SPT system in one and two spatial dimensions. Using a specific example of symmetry-enforced Kitaev chain in one dimension, I will discuss how deconfined quantum criticality can emerge in a LSM-SPT system.