It’s a good time to summarize my 2022 journey of apprentice as a theoretical physicist. It’s my first year of doctoral course (in a Japanese university, the first year doctoral course, or D1, corresponds to the third year of the graduate school in the US). I will organize this year-end review into two sessions:
- one is related to my PhD research topic, and
- the other is about learning all areas of physics, not just limited to my current research topic.
Why do I divide my life in doing physics into two parts? The truth is, I’m not sure, and I’m still trying to understand this. However, it is a convenient and practical division, roughly corresponding to the “work-life-balance” idea. As an animal, we need basic needs to survive, including clothing, eating, living and moving (衣食住行 in Chinese). To me, this is core to the idea of working, and is related to my first division about my PhD research topic. In this sense, the first part is like my duty or job. The second division is more about interest and enjoyment. I got this idea after reading Bertrand Russell’s essay, In Praise of Idleness, back in 2021, where he discussed work and idleness.
So much for the introduction, let’s start with the second division about what I was learning during this year.
Contents
A. Interesting physics I learned this year
The two keywords of this year’s study in physics are
quantum
and
relativity.
For me, the strongest motivation for returning to these two basic topics is my continuous failure of understanding general relativity (GR), quantum field theory (QFT), conformal field theory (CFT), many-body physics, and their relationships (for example, how a field theory description arises from a discrete lattice model of a many-body system?) It is so frustrating, so I decide to understand better about these two more basic topics.
Besides this personal motivation, these two topics itself is very rich and interesting! Quantum world is like Alice’s wonderland.
A-1: Quantum strangeness
The more I learn about quantum world, the more strange I find it to be. Here is a list of what I learned about this weirdness of quantum world this year:
- Preskill’s Quantum Information notes (from April to now). This topic is a collision of quantum physics, computer science and information science. In one sentence, it is to harness quantum superposition and entanglement to change of our understanding of the nature of computation and information. Very luckily, our research group chose this as our textbook reading material this year from April and we are now trying to understand how to hide quantum information using entanglement.
- Alain Aspect’s quantum optics course on Coursera (from July to August). Right before Professor Aspect got his Nobel Prize in October this year, I finished his second excellent course on quantum optics. It is a realization of quantum strangeness in lab!
- Jim’s edX quantum mechanics course (from August to September). I love the first part of this course, full of thought experiments demonstrating the strangeness of the quantum world. The most mind-boggling would be the interaction free detection using quantum superposition! Here is a quick introductory video on this in Bilibili (I added Chinese subtitles) or YouTube. Also see chapter 4 of Scott Aaronson’s notes.
I discussed these three courses in my previous post in September this year.
The above three courses focus on the strangeness of the quantum world and the physical picture and intuitions. I also took the following relatively more advanced courses, focusing on combining quantum with other things like relativity or many-body physics:
- Murayama’s QFT video lectures (During May; start this because I showed a video of Murayama to Tetra, trying to convince her of the charm of physics, but ending up so fascinated about his explanation myself ). This should serve as one of the preparations for my future attacking of a standard QFT textbook. The best part of this course is that the connection between QM and QFT is made very clear from the very beginning. Murayama then moves on and talks a lot of physical examples that can be analyzed using QFT, including Bose-Einstein condensation (BEC), superfluidity, BSC theory of superconductivity. All of these examples are based on a non-relativistic theory, so the field Lagrangian is closely related to the Schrödinger equation. There are also several very intense and bizarre phenomena. One is Bosenova, which is an implosion in a Bose gas system, very much the supernova. One more is Schwinger limit and Hawking radiation, which are basically creating matter from the vacuum. In later part, QED and Dirac theory are also introduced, and scattering process up to tree-level is discussed. I believe the later part would be more interesting when learning a standard QFT book in the future. In summary, the physical picture is made crystal clear in this first QFT course. A good next step would be McGreevy’s QFT lecture series, A, B and C during 2021 to 2022.
- Sachdev’s Quantum Theory of Solids of Harvard Physics 295B (From end of October 2021 to the beginning of February 2022). This is a standard course on quantum many-body theory. The powerful Hartree-Fock method is applied to consider the interaction, based on a free theory. I got very familiar with Feynman diagram and how it is related to physical process in a metal. I plan to read the textbook related to this course and finish some exercises in the textbook to get a deeper understanding. The next step should be Sachdev’s Quantum Phases of Mater of Harvard Physics 268R and his IAS course. It would be a good idea to want for his new book to come out first, since the video lectures are in parallel with his new book. Another is McGreevy’s lecture videos about SPT phase. I have a previous post discussing this course.
- Vidal’s PSI course about condensed matter physics (From June to July; started this because I want to understand more about spatial symmetry, like translational and reflection symmetries in quantum spin systems). It is also about quantum many-body theory, but focused more on spin systems and numerical techniques to analyze them. The numerical method like exact diagonalization forces me understanding a lot about quantum spin chains and their correspondence to free fermion systems. And I now have a better understanding of the correspondence between the spin picture and fermion picture, which puzzled me a lot when discussing the Gamma Matrix model with Wei-Lin previously. I plan to write a note about this course and also write a post in this website in the near future.
A-2: Relativity and classical physics
As I mentioned in a previous post, I started revisiting relativity because I had endless difficulty understanding a standard quantum field theory (QFT) or conformal field theory (CFT) book. One of the important ingredients in these two topics are spacetime symmetry. There are many notions like energy-momentum tensor that I’m not familiar with. I need more physics background on these. So, I decided to revisit special relativity and possibly then continued to finish a general relativity course. Also, I believe it is a good way for a physics student to learn basic differential geometry. Here is a list of courses I took this year, related to this topic:
David Kubiznak’s PSI course called Theoretical Mechanics (finished during end of March). This is a short course, formulating the usual Newtonian mechanics using the language of differential geometry, including manifolds, vectors, tensors, Lie derivatives and differential forms. The conservation laws have a total different form in this language. I believe it is a good starting point to connect what I know well to what I want to know but still don’t know, like QFT and CFT. The next step should be Arnold’s classical book: Mathematical Methods of Classical Mechanics.
- Spacetime Physics by Taylor and Wheeler (from August to September, see my previous post). This is my favorite physics textbook of 2021, sitting way up at the top of the list. I simply love Wheeler’s way of explaining physics, so clear, so deep and so considerate and student-friendly. It clarifies most of my long-standing confusing about this topic. Reading this book is like reading a thrilling novel like Sherlock Holmes: you cannot wait to see what happens next! BTW, Terry Tao, the genius mathematician, also mentioned this excellent textbook in his December post about special relativity this year.
- A first pass of general relativity; I mainly follow Prof. Scott Hughes’s MIT’s physics graduate course 8.962, and also the textbook by Schutz (I started in middle July, and is still on my way). After finishing Taylor and Wheeler’s textbook, I cannot wait to starting a full general relativity course. I tried this course during the end of 2020, but it was interrupted then. For Prof. Hughes’s video lectures, I’ve finished the half part, up to Einstein’s field equation. Then, I paused for a while, went back to Schutz’s textbook, read the corresponding chapters and selected some exercises to deepen my understanding of the concepts derived in Prof. Hughes’s video lectures. I feel that I’m more comfortable about the difficult notions like parallel transport and Riemann curvature tensors. Next, I will move on to attack the second part of the course: application of this beautiful theory under 1) the weak field limit, so we get corrections to the old Newton’s gravitation theory and 2) presence of very high symmetries. This sounds very interesting to me.
- Taylor, Wheeler and Bertschinger’s book: Exploring Black Holes (Study in parallel with Schutz’s book). This is a low-level GR textbook, again, focusing on physics picture. The idea is to write down the solutions of Einstein’s field equation and try explaining its physical story behind each solution. The style is just like the Spacetime Physics. Love it.
So much for the physics I learned, let’s move on to the summary of my research topic.
B. How about my research life?
I entered D1 in October 2021 and decided to explore several research topics at the same time for the first year, partly because I had been stuck to my previous topic for a while so I wanted to explore something different.
In summary, here is a list of what I have been tried during this year. I will be a little vague here, since all of them are ongoing projects and we haven’t understood much about them yet.
- Direction generalization of my Master’s topic from 2D to 3D, also tried a naive design unique to 3D problems (from October 2021 to March 2022). This is the quick-and-dirty approach to 3D. But, not quick in particular, since 3D implementation and calculations took more time. The current conclusion is that our previous method works in 3D, but current dirty implementation doesn’t give satisfactory estimation accuracy.
- Try finding an exact tensor-network representation of a critical fixed point (from October 2021 to March 2022). My professor suggests this to me back in September 2020, and a recent work by Rychkov and Kennedy let us rethink about this idea. We started with the Lagrangian corresponding to the free boson CFT, but the problem is way harder than we originally thought.
- A topic suggested by Wei-Lin, a postdoc in our group, about a 2D exactly-soluble spin model called Gamma Matrix Model (from October 2021 to the end of December 2021). This is a generalization of the famous Kitaev model, which supports non-abelian anyons that are crucial for fault-tolerant quantum computing (sounds difficult and cannot understand? I felt the same way 😅🤪). I think it is a good way to study the Kitave model, so I tried. But, later I found I might need more prerequisite basic knowledge about simpler quantum spins systems. Luckily, we have made a successful first step. It is just I need more understanding about this physical system in order to get more motivation to continue this topic. Also, this topic is one of my motivation to study Sachdev’s Physics 295B course and Vidal’s PSI course, mentioned above. I might try returning to this topic in the future to see whether I’m prepared for it, or what other things I need to learn in order to proceed.
- About applying the TNRG method to anyonic systems (from February to June). This is a suggestion from Iino-kun, a formal PhD student in our group who graduated in March 2021. One of the problem I want to do is to impose the global symmetry of the anyonic system in numerics. I tried to start with studying how the global on-site symmetry like U(1) or SU(2) are imposed in TN language and also studying Markus Hauru’s previous paper about topological defect and TNR. However, I still don’t have a clear idea how to achieve this. As a first step, maybe, I should just use the ordinary TNR method to do a quick calculation without worrying about the topological symmetry of the model. This is one of my motivation to revisit Vidal’s PSI course and reimplement and study Evenbly’s TNR design.
- Restart my 3D project and refine my previous quick-and-dirty approach (from July to now). This has been my current focus after entering the D2 year from October this year.
Always learn something new and valuable from your blog, my friend. Have a good year!
🥳🥳🥳 Good luck too!!!
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