Junchen Rong's site

The large charge section of O(3) satisfies a formula predicted by effective action.  In [1], we measure the universal constants in the formula using numerical bootstrap.  The numerical data also allows us to perform conformal perturbation to study another important theory called the Cubic CFT. For a more comprehensive review of this work, see my slides [2].

Using the mathematical result on the classification of finite subgroups of the O(5) Lie group, we classified the irreducible perturbative fixed points of five scalars' field theories. See my talk "Towards classifying perturbative fixed point in 4-eps expansion" (or here) and the paper [1].

Here are some Monte Carlo simulations of the quantum Heinsberg models.  In particular, the quantum phase transition of the bilayer long-range Heinsberg model is governed by a non-traditional QFT where space and time have different scaling behavior, see the papers [1] [2] 

In Monte Carlo simulation, the size of the lattice can be also interpreted as the scale of a renormalization group flow.  Combining the recent results on Cubic CFT with quantum Monte Carlo simulation, we discovered a new phase of the fully packed quantum loop model on a triangular lattice. See my talk "Conformal field theory approach to quantum loop models" and the paper [1].

The usual phase transition consists of a high-temperature disordered phase and a low-temperature ordered phase. However, more exotic inverted phase diagrams are possible with the help of certain conformal field theories. See the talk "Spontaneous breaking of finite group symmetries at all temperatures" and the paper [1].

The Migdal-Polyakov bootstrap approach was the first approach used by physicists to study critical phenomena.  Using the modern technique to evaluate Feymann integrals, we revisited this program. Check the talk "The Old Conformal Bootstrap Revisited" and the paper[1].

Conformal bootstrap is a method to constrain the scaling dimension of CFT operators, when applied to the super-Ising model in 2+1 dimensions, it lets us determine certain conformal data to high precision.  For details, check my talk "Bootstrap minimal superconformal field theory in 2+1D" and the papers [1] [2] [3].

Here are the links (lecture I, lecture II) for a short lecture on "the conformal field theory approach to (quantum) phase transitions" that I gave during the "Hong Kong Computational and Theoretical Physics Study Group".

Some of the materials covered in these lectures are included in the review/lecture note I wrote on Scalar CFTs from structural phase transitions.