Chapter 494 Fatal Flaws in the Paper

The end of the report does not mean that the report meeting is over.

For the report meeting of natural sciences such as mathematical physics, the question-and-answer session is the real challenge.

For many researchers, submitting a conference paper is stressful, and answering questions is even more difficult.

Because the reporter not only has to answer questions from everyone present, but sometimes those questions are often long speeches with pretentious modesty, scattered self-statements and undisguised intellectual show-offs.

Simply put, you may encounter some pretenders during the question-and-answer session.

Of course, this situation is impossible in Xu Chuan's report meeting.

After all, in terms of pretending, cough, in terms of advanced operations, who can beat him in his report meeting?

When the applause in the auditorium weakened a little, Xu Chuan stood back at the report platform, picked up the microphone and spoke again:

"The report on the unified framework of strongly correlated electron systems ends here. If you have any questions, please feel free to ask them, and I will do my best to answer them."

For the strongly correlated electron system and the physics community, the most important thing is the introduction of the concept of dimensional space in the entire paper and the corresponding mathematical methods.

If you can master these things, then it is not difficult to understand this paper.

As Xu Chuan's voice fell, arms in the auditorium were raised one by one.

Starting from the front row, Xu Chuan began to answer questions.

In this kind of report meeting, the selection of people is naturally arranged by the reporter himself.

The first questioner was Frank Wilczek, the winner of the 2004 Nobel Prize in Physics, who mainly engaged in research in the fields of condensed matter physics, astrophysics and particle physics.

This big guy asked two questions related to the calculation methods of low-dimensional mathematical theory, and sat down after getting the perfect answer from Xu Chuan.

The second one who followed closely was Michael Kosterlitz.

The research direction of this 16-year Nobel Prize in Physics is mainly condensed matter theory and one-dimensional/two-dimensional physics.

When Xu Chuan signaled him to ask questions, Kosterlitz quickly stood up and took the microphone from the staff with some excitement and expectation.

"When the electron-electron correlation interaction is introduced into topological quantum materials, a complex novel ordered phase will be generated in the system, but how to explain this mathematically is still a mystery."

"May I ask how Professor Xu sees this problem? Does it have a strict model and analytical solution?"

As a scholar studying topological phase transitions and topological phases of matter, he has been looking for a way to unify topological phase transitions and strongly correlated electronic systems.

But unfortunately, even if he can start from mathematics and use topology to study topological phase transitions and topological phase materials of physical materials, he still can't find a suitable way.

Now, he sees the hope of a breakthrough in this young scholar on the stage.

Of course, what he doesn't know is that the road he longs for and hopes for has already been opened up.

At the report platform, Xu Chuan immediately knew the other party's idea when he heard this question.

Establish a unified theory for topological phase transitions and strongly correlated systems, and then conduct in-depth research on topological quantum materials.

This is the work he was still busy with a few days ago, but he didn't expect that someone would think the same way as him today.

After a pause, Xu Chuan said, "This is one of the unsolved problems in the strongly correlated system. Unify the strongly correlated system and the topological state."

"In theory, it is possible to unify the topological state into the framework of the strongly correlated electronic system, but I have not studied this aspect in depth. Perhaps you can consider the non-trivial multi-band quantum geometry method of hybrid hybrid orbital characteristics."

"This route has now shown many physical phenomena, which can also be explained by mathematical methods, and perhaps it can be extended and expanded."

Although he has completed this theory, he cannot state it clearly, nor can he explain his own paper.

After all, topological quantum materials involve the research of quantum computers, which is of great importance.

But at the report meeting, fellow scholars in the audience had already raised questions, and he could not say nothing at all.

Listening to Xu Chuan's answer, Professor Kosterlitz fell into thought and sat down unconsciously.

Seeing this, Xu Chuan skipped him and continued to ask questions.

And the person who stood up next was Professor David Gross, the director of CERN.

Like Frank Wilczek, he is also the winner of the 2004 Nobel Prize in Physics.

And nominally speaking, this great man is also Xu Chuan's ancestor.

Because he is Witten's mentor, theoretically, he is at the same level as Alexander Grothendieck.

Of course, in terms of influence in their respective fields, Gross is definitely not as good as Grothendieck. After all, the latter is known as the founder of modern algebraic geometry and the greatest mathematician of the 20th century.

But Professor Gross's achievements are not low, and can even be said to be very high.

He is the founder of "hybrid string theory", the founder of asymptotic freedom in the theory of strong interactions, one of the main founders of quantum chromodynamics, and a recognized leader in modern physics.

In today's physics community, his status is not to say that he can compete for the top three, but it should be no problem to compete for the top five.

This time he came here, on the one hand, the unified framework theory of strongly correlated electronic systems is indeed within his research scope.

On the other hand, he was preparing to connect with Xu Chuan to communicate with CERN and China on the cooperation in the construction of the Large Hadron Collider.

Although CERN is still debating whether to continue to build the high-brightness LC-LHC hadron collider, I am afraid that there is not much hope.

With the rise of China, the decline of the United States and the European Union is inevitable.

In the economic downturn cycle, the importance of the Large Hadron Collider, which is a huge cost, extremely troublesome to maintain and requires a huge amount of money, is not so high.

Of course, the questions he raised at the report meeting today are definitely not related to the collider, but only to the strongly correlated electron system.

After all, this is the unspoken rule of the report meeting, and it is also the necessary respect and etiquette for academic reporters.

Standing up, Professor Gross thought for a while and organized his words before speaking: "On page 31 of the paper, I noticed the topological insulator effect formed by the strongly correlated electron effect in the two-dimensional state you proposed."

"This study first proposed the minimum continuous model of the p+ip exciton phase and proposed a new topological invariant, the chiral Chern number, to characterize the topological properties of the system."

"But in the two-dimensional minimum two-component model, although the traditional Chern number of the topological exciton insulating phase is zero, it has half the chiral Chern number. Can the reporter explain this point?"

Hearing this, Xu Chuan lowered his head and flipped through the paper: "Page 31?"

"In short, this new topological invariant The p-ip insulator is formed by the condensation of excitons of the p+ip wave function, and its mechanism is similar to the condensation of p+ip wave Cooper pairs that leads to the famous topological superconductor. "

"And there will be Majorana fermions in the vortex of the topological superconductor, and there will be quasiparticles with 1/2 charge in the vortex of the topological exciton insulator. But unlike the p+ip topological superconductor and Chern insulator, the traditional Chern number of this new topological exciton insulator is zero, so its topological properties are characterized by the "chiral Chern number" newly proposed by the research team. "

"In addition, the condensation of p+ip excitons will also lead to the breaking of in-plane spontaneous magnetization and time reversal symmetry"

Professor David Gross interrupted him before Xu Chuan finished speaking.

"I know these, what I want to know is how you define that strong electron-electron interaction will produce a scattering channel with p-wave symmetry. "

"If I remember correctly, this part of the theory involves small polarons in the strong electron-phonon interaction system, but this is still an unresolved problem. "

Standing in the audience, David Gross looked at the young man on the podium and slowly expressed his doubts.

His voice was not loud, but it exploded in the entire auditorium like a thunder, attracting the attention of everyone present.

Hearing the question from his mentor, Edward Witten's dark green pupils instantly condensed, and his breathing became rapid.

This was a defect that he had not discovered, and even the entire physics community was afraid that few people had noticed this extremely subtle key point.

Professor Michael Kosterlitz, who was sitting next to him and had just asked the question, was stunned for a moment, then quickly bent down and took out the paper from the backpack placed on the corner of the chair, and found the 31st page of the paper.

Looking at the theories and mathematical formulas in the paper, he quickly calculated in his mind.

The problem of small polarons in the strong electron-phonon interaction system is a problem in the strong interaction system. It was once widely and deeply studied in the 1960s to 1980s.

But with the discovery of strong electron-electron coupling systems represented by high-temperature superconductors, research in this area is no longer mainstream. There is no complete set of theoretical images to uniformly solve this problem.

He did not expect to find this deeply hidden point in this paper.

Now, for Professor Xu, this may be a "fatal" flaw in the unified framework of strongly correlated electron systems.

PS: There is another chapter in the evening