Great Country Academician

In the living room, Xu Chuan and Mr. Yang exchanged some research directions of strongly correlated electronic systems.

It has to be said that although this old man is nearly a hundred years old, his thinking is still quite clear, and he can rely on the knowledge in his mind to screen and rule out many directions.

This is extremely rare for a centenarian.

For Xu Chuan, although these exchanges are just some research directions and theories, they can still save him a lot of time and point out some directions, which is not a small gain.

On the side, Qiu Chengtong, who was listening to his communication with Mr. Yang, suddenly interjected: "Although condensed matter physics is not within the scope of my research, why don't you regard the electronic behavior in the strongly correlated electron system as an electronic liquid or an electronic solid? "

"Such as Rattinger liquid, liquid crystal state, charge density wave, Wigner crystal, etc., perhaps explained from this aspect, can achieve the purpose you said?"

"E-liquid?"

Old Mr. Qiu interrupted abruptly, causing Xu Chuan to look at it suspiciously.

I saw this old gentleman who is famous for mathematics continue to explain: "Although my main research direction is not physics, I know that based on the idea of ​​topological core rotation, the unified mathematical theory of quantum liquids has been developed. Including topological order, SPT/SET order, symmetry breaking order and CFT-like gapless phase, etc.”

"If you can explain the topological skeleton and local quantum symmetry of quantum liquids, and show that all n quantum liquids form a -condensed complete higher category whose equivalent type can be explicitly calculated from the simple co-sheet 1-category, perhaps Do what you need?"

"Starting from the field of quantum liquid?"

These words made Xu Chuan stunned for a moment, and fell into deep thought.

The strongly correlated electron system comes from the interaction of electrons, and there is no correlation between the motions of electrons without interaction.

Simply put, if the interaction is strong, the correlation is strong, and if the interaction is weak, the correlation is weak. Here, "strong" and "weak" refer to relative size, not absolute size, and depend on the competition between different energies within the system.

The same interaction is not the same for half-filled bands and full bands, or for massive electrons (flat-band electrons) and massless electrons (Dirac fermions).

In condensed matter physics, the behavior of the electron system can usually be regarded as a gas (free electron gas).

The "electrons" here can be quasiparticles, such as conduction-band electrons in crystals, or single-particle excitations in other interacting systems—that is, they are originally liquids, but can still be regarded as gases through simple approximations.

After all, when the interaction is small, it can be approximated by free electrons; when the interaction is large, a Mott insulator will be formed, and the degree of freedom of electron motion is frozen, only the degree of freedom of spin.

At this time, a large degree of freedom can be expanded to obtain an effective spin model.

From this point of view, it is indeed feasible to regard the locked electron movement in the strongly correlated electron system as liquid or solid.

It's just that he couldn't figure out how to take this road for a while.

After all, it often takes quite a long time from idea to research.

On the other side, in the living room, Mr. Yang and Mr. Qiu did not bother Xu Chuan, who was deep in thought, and each was thinking about other directions and ideas.

The purpose of today's exchange on strongly correlated electronic systems is to provide some ideas and directions for the young scholar in front of him, which they can still do.

As for the more specific calculation, I am afraid it will depend on him.

Whether it is Mr. Yang or Mr. Qiu, at their current age, it can be said that they have almost no energy to complete such calculations of top-notch and cutting-edge problems.

Even in the first two years, Mr. Qiu still had the energy to study and advance the KZB equation problem.

But as the years go by, people age faster and faster.

Science is always young, and these old people who have sunk into the sky are no longer able to advance new knowledge.

In the living room, Xu Chuan pondered for a long time before he came back to his senses.

Seeing his movement, Mr. Qiu looked over first, and asked curiously, "How is it?"

Xu Chuan thought for a while, and said: "I have a little idea. As for whether it can be done, I will study it later. I thank you for your ideas and theories today. I really trouble you."

Mr. Qiu smiled and said, "This is nothing troublesome, as long as it helps you."

After a slight pause, he continued: "Of course, I'm not very familiar with the direction of physics. You don't need to stick to my theory. Maybe it's wrong."

He was getting a vaccination in advance to prevent Xu Chuan from sticking to the direction he proposed. After all, he is not a pure physicist, and condensed matter physics is not within the scope of his research.

Xu Chuan nodded with a smile, and said, "Don't worry, I've never been a person who sticks to one road. When I feel that this road doesn't work, there is a high probability that I will give up on it."

"But now, I think it is still possible to give it a try, at least I think it should be feasible, and I feel that I can see the end."

On the opposite side, Mr. Yang seems to have remembered something, and suddenly said: "Is this the scientific intuition of a genius when he was young?"

After a slight pause, he continued: "When I was studying the Yang-Mills equation before, when I tried to extend gauge invariance to non-commutative groups, I tried many methods, but failed many times."

"Because U1 symmetry is commutative symmetry and SU2 symmetry is not commutative symmetry, I have been stuck for a long time. Until one time when I decided to add a quadratic term, I only made this idea at that time, and I couldn't help it in my mind. The idea was born that this was the right way.”

"It was soon confirmed that this idea was correct, and successfully led to a new field theory."

After a pause, he then said with emotion: "It's just a pity that in the subsequent research, I almost never had this kind of abnormal clarity, as if I can see the correct answer as long as I think about it."

As he said that, he looked at Xu Chuan, asking and saying: "I used to never understand why you can make such brilliant achievements at this age, but now it seems that you can often have this intuition when researching problems. ?”

Hearing Mr. Yang's emotion, Xu Chuan froze for a moment.

He seems to have this intuition too?

And not once or twice. When studying mathematics before, whether it was studying the Hodge conjecture or the NS equation, he could always rely on this feeling to judge whether the following path was appropriate at key points.

Of course, it is unrealistic to say that the correct answer can be seen at a glance.

But indeed, this feeling helped him save a lot of time.

In the past, he always felt that this was a judgment brought about by the knowledge in his mind, but now listening to Mr. Yang, it seems a little different?

On the side, old Mr. Qiu smiled and said, "Don't listen to his nonsense, what scientific intuition, what he talks about is so metaphysical, it's just the experiential feeling brought by knowledge."

"The group of them who are engaged in physics have all developed towards theology in the end. This old guy has this trend a few years ago. Don't listen to his foolishness, you boy, just do your own research seriously. This kind of thinking depends on it, sows will climb trees."

Hearing this, Xu Chuan coughed in embarrassment.

He seems to be doing physics.

PS: Ask for a monthly pass at the second watch.

Cough cough, originally it was the third update today, but I found that I overestimated my own strength. It took a lot of time to check the information and understand the information and papers today, let’s make it up later ˋ(°▽,°)