Determining the long-range phase of matter of a strongly coupled system from its microscopic description has long been one of the central topics in physics. Lattice bootstrap is a recent method that utilizes the model’s specific microscopic equations of motion and draws rigorous constraints on its macroscopic properties. In this talk, I will briefly review some of the recent successful examples, and discuss our ongoing project of bootstrapping spacial lattice with real time. We take the (1+1)D transverse field Ising model as an example, but the method is general. We show that the Hamiltonian equations of motion and the non-negativity of the norm of states provide crossing equations constraining the mass gap in the thermodynamic limit. We obtain preliminary results as a proof-of-principle that such constraints exist. Host: Yuan Xin (yuan.xin@yale.edu)