(2023-06-01) Ordinary phase transitions happen between 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 [Arxiv]. 

(2024-09-18) In a recent paper, we studied this problem using functional RG [Arixv], and showed that indeed some quantum field theory models would show persistent order that is unmeltable, building on the genius idea in [Weinberg, 74] and [Chai et al, 2020].

(2024-12-16) In [paper] by Zohar Komargodski and Fedor K. Popov, the authors rigorously established that persistent order exists. This phenomenon may have important applications in many areas of physics. Imagine that we have a new phase of the standard model that persists to an infinite temperature (also called "symmetry non-restoration"), this will change the history of the universe (see, for example [1] [2] [3][4]). If we can construct a model where the BKT phase can persist to an infinite temperature, we get a high-temperature superfluid. It is time to re-investigate the application of persistent order to early universe cosmology and condensed matter physics!

(2025-01-16) Today, a popular science article covering the story of persistent order appeared in the Quanta Magzine. Our work was briefly mentioned.

(2022-10-22) In Monte Carlo simulation, the lattice's size can be 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 [Arxiv].

(2024-12-03) In [Arxiv], we studied the finite-temperature phase diagram of the Quantum Loop model. The vison-plaquette phase previously discovered is shown to persist to a finite temperature. One can study the finite temperature phase transition by considering putting the conformal field theory on S1*R2. See a recent talk titled "From the Cubic CFT to the Quantum Loop model" that I gave.

(2024-06-15) Recently, I introduced a new perturbation theory to study conformal field theories, which involves performing the well-known long-range perturbation theory and then imposing the local conformal Ward Identity to recover the conformal data of the local CFTs.  This method works perfectly for the O(N) vector models in 3D after properly re-summing the long-range perturbation series. [Arxiv] 

(2024-09-18)  We need to properly re-sum the asymptotic perturbative series to approach the strong coupling region. The large-order asymptotics of the series are controlled by a soliton of a nonlinear equation with fractional Laplacian, which was first written down in a famous paper by E. Lieb. This suggests that the perturbative series is Borel re-summable.

(2025-01-30) These long-range quantum field theories are also important in statistical physics, for the interaction among particles on the lattice is usually long in nature. 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 [Arxiv_1] [Arxiv_2].

(2023-01-09) 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 [Arxiv_1] [Arxiv_2] [Arxiv_3].

(2023-11-16)The large charge section of O(3) satisfies a formula predicted by effective action.  We can measure the universal constants in the formula using numerical bootstrap.  The data also allows us to perform conformal perturbation to study another important theory called the Cubic CFT.  [Arxiv][slides]

(2025-01-30) The word "bootstrap" here means to lift up oneself by pulling one's bootstraps. It is interesting to see this metaphor appearing in different cultures, in ancient China, there is a story of a general (项羽) who is so strengthful that he could sit on a chair and lift the chair (and himself) up. In conformal field theory research, the word "bootstrap" means a method by which one can solve a system purely relying on self-consistency conditions.

(2023-06-09) Using the mathematical result on the classification of finite subgroups of the O(5) Lie group, we classified the stable 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 [Arxiv].

(2025-01-30) The classification of perturbative CFTs in 4-epsilon expansion involves solving a set of polynomial equations. The standard way to attack this type of problem is to calculate the so-called "Gröbner basis". It may be possible that a quantum computer can speed up the calculation!