QST Seminar - Conformal symmetry, Optimization algorithms and the Critical Phenomena

In the phase diagram of many substances, the critical points have emergent conformal symmetry and are described by conformal field theories. Traditionally, physical quantities near the critical point can be computed by perturbative field theory method, where conformal symmetry is not fully utilized. In this talk, I will explain how conformal symmetry can be used to determine certain physical quantities, without even knowing the fine details of the microscopic structure. To compute the observables precisely, one needs to develop powerful numerical techniques. In the last few years, we have invented many computational tools and algorithms, and predicted critical exponents of Helium-4 superfluid phase transition and Heisenberg magnet to very high precision.