Nancarrow: Coarse-grained Bootstrap of Quantum Many-Body Systems

Since the success of the conformal bootstrap in computing the physical data of the critical 3D Ising model, bootstrap methods have enjoyed renewed interest due to their ability to compute rigorous bounds on observables in strongly-coupled systems. I will report on recent progress on bootstrapping quantum many-body systems in 1+1D. Whereas other methods such as DMRG/MPS seek to systematically approximate a state vector in order to compute physical quantities, a bootstrap seeks to impose a hierarchy of constraints on those quantities directly. While the system in question obeys an infinite set of constraint equations, this set can be truncated by considering only those constraints pertaining to smaller subsystems. In the context of the many-body problem, this allows us to work in the thermodynamic limit even with finite computational resource. The systems of constraint equations, however, grow exponentially in the subsystem size. By using tensor networks to coarse-grain these constraints, we are able to substantially augment the extent of the subsystems considered and thereby compute much tighter bounds on observables than achievable with previous methods.