Blogish

March-14-2025:

I would like to share my failed attempt to construct a lattice model for persistent order. Onsager in 1949 developed a model for the Isotropic-Nematic Transition of liquid crystal. By placing hard rods in space (say, a 2d plane), as we increase the density of the rods, the system will go from an isotropic phase to an nematic phase. The physics is pretty simple: as the density increases, the rods start to block each other. The lattice analogy of the model is the k-mer model. The so-called k-mer is just a rod occupying k lattice sites. We can introduce a chemical potential to favor higher density at higher temperature. Naively, this model should give us an ordered phase at high temperature. This idea, however, failed because at extremely high density, the problem reduces to the tiling of 2d phane; it is known that there are infinitely many ways of tiling. See my discussion with Google Gemini about the problem.

Feb-26-2025:

I always thought that the story of persistent symmetry-breaking order at infinite temperature is a quantum field theory phenomenon/artifact. Recently, papers [1] [2] by Zohar Komargodski and colleagues have changed my mind. They found lattice models that support persistent order. The models are surprisingly simple; one just needs to replace the Ising spin with a lattice variable that can take values in all nonnegative integers. For lattice models, the field-theory approximation only works when you are infinitely close to a second-order phase transition. In condensed matter systems, it is very easy for temperature to approach a scale at which the field-theory approximation stops working. These recent works have bypassed these caveats and brought the phenomenon to a whole different level of reality.

Sep-18-2025:

I am considering the resummation of the perturbative series in the 4-eps expansion for CFTs beyond the scalar theory. This led me to find the book "Large-order Behaviour of Perturbation Theory" edited by J. C. Le Guillou and Jean Zinn-Justin, where they wrote an amazing review of the early results. It looks to me that we should recycle these results to re-sum Gross-Neveu-Yukawa and QED.

Jul-1-2025:

I recently heard about an exciting experimental realization of U(1) Dirac spin Liquid. The experimental signature seems to be cleaner than that of Herbertsmithite, as reported in this paper. Using ultra-cold inelastic neutron scattering, they were able to "see" the Dirac cones directly. For field theorists, U(1) Dirac spin Liquid is the 2+1-dimensional QED coupled to four complex two-component fermions.

May-4-2025:

The lecture notes for my lectures on "Introduction to 2+1D conformal field theories" can be found here. The notes are under construction. Please be aware that it may contain typos, and references are incomplete.

Apr-16-2025:

The ITensor package is super powerful and super easy to use. Here is an example code to calculate the entanglement entropy, 2pt and 3pt functions of the critical transverse field Ising model.

Feb-28-2025:

A popular science article for the WeChat account "返朴"，"热量会破坏一切，但物理学家找到例外"

Feb-14-2025:

I found ChatGPT more and more useful in my daily research. It can help me solve research-level problems. The way it works is actually very much like the human brain. You have to ask a few preparatory questions so that chatGPT knows the background of the problem. When you feel that it knows the problem as well as you, you can then ask about your research problem. Here is a conversation between me and ChatGPT about the lattice realization of a deformation of tricritical Ising CFT that preserves a certain non-invertible symmetry. I am genuinely amazed, and I do not know what the world will be like in 20 years.

Jan-28-2025:

There is a paper on Arxiv titled "Phase Transitions in Large Language Models and the O(N) Model". I am very curious about what this is.

Jan-02-2025:

Today I watched the movie "Her Story" by Yihui Shao. Amazing movie!

Dec-20-2024:

I recently watched two videos by Phymaths, one of Zohar Komargodski, and another of John Donoghue. The former contains various thoughts on many deep topics in theoretical physics. The latter, on the other hand, discussed more on the traditional approach to quantum gravity. I highly recommend both interviews!

Dec-20-2024:

Renormalization group flow has been the center of my research for many years. The site Physics of Scale collects the interviews of many early heroes of critical phenomena. The interview with Alexander Patashinski contains some interesting stories about the communication between physicists from the West and the Soviet Union during the time of the Cold War.

Dec-20-2024:

There are many interesting articles in Quanta Magazine, such as "A Fundamental Theory to Model the Mind" and "When Does the Brain Operate at Peak Performance?". The articles are about the hypothesis that the human brain is a system of so-called self-organized criticality. Self-organized criticality is nothing more than a CFT without relevant operators.

Dec-16-2024:

Google's NotebookLM is super fun! This is a podcast about "persistent order" generated from three papers [1][2][3].