Our large-scale simulations reveal a rich phase diagram, establishing the existence of three distinct insulating phases whose appearance can be controlled by tuning different types of interactions between the electrons. The first phase, called a quantum valley Hall state, has an insulating bulk and a dissipationless electronic current on its edge. The second phase, called an intervalley coherent state, is an insulator in which electron pairs emerge that behave in the same way as in a ferromagnet. The third phase, called a valence bond solid, is a phase realized in single-layer graphene if there were strong Coulomb interactions and electrons with degrees of freedom beyond just charge and spin (known as multiflavor electrons).

These results offer an unbiased solution for pristine TBG at charge neutrality, that is, the system has no extra electronic charge, and serves as the foundation for explanation of the more exotic behaviors of this fascinating material.

Full Article: https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011014

]]>Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search of knowledge, and unbearable pity for the suffering of mankind.

—Bertrand Russell

As Russell nicely put it, scientists are often driven by strong passions for the search of knowledge, such search not only benefits the human society, but often times brings the ecstasy to themselves -- the ecstasy for instance of understanding the hearts of men, knowing why the stars shine, and apprehending the Pythagorean power by which number holds sway above the flux -- that is so great that scientists would often have endured the long hours of working and sleepless nights for the pursuit of such joy.

The Landau’s theory of Fermi liquid (FL) (Note 1), established in the first half of the 20th century, is the foundation of the scientific and industrial usage of the metallic materials in our society. It is also the basis of our current understanding of metals. However, in the second half of the 20th century, more and more metallic materials were discovered which behave very differently. The non-Fermi liquid (NFL) behaviour of these “strange metals” remains a puzzle to physicists, and there is no established theory to explain them.

Recently, a joint research team comprising members including Dr Zi Yang MENG, Associate Professor of Department of Physics at the University of Hong Kong (HKU), Dr Avraham KLEIN and Professor Andrey CHUBUKOV from the University of Minnesota, Dr Kai SUN, Associate Professor from the University of Michigan, and Dr Xiao Yan XU from the University of California at San Diego, has solved the puzzle of the NFL behaviour in interacting electrons systems, and provided a protocol for the establishment of new paradigms in quantum metals, through quantum many-body computation and analytical calculations. The findings have recently been published in Npj Quantum Materials. The work was supported by the Research Grants Council of HKSAR, and the Ministry of Science and Technology of China.

The Landau’s theory of Fermi liquid (FL) successfully explained many features of simple metals like Copper, Silver, Gold and Iron, such as when temperature changes, their resistivity, heat capacity and other properties follow simple function form with respect to temperature T (for example, resistivity follows ρ~T^{2} and heat capacity follows C~T, independent of material details). The success of the Fermi liquid theory lies in the central assumption that the electrons, the droplets in the Fermi liquid are not interacting with each other, but behave identically in the material.

However, many metallic materials which were discovered after FL was established, do NOT behave as FL. For example, in the so-called high-temperature superconductor compounds - copper oxides and iron pnictides - their resistivities are linear in temperature ρ~T before the system becomes superconducting (resistivity is then zero), and such systems are in general dubbed Non-Fermi-Liquids (NFL). Different from the simple FL, the electrons of NFL, the droplets, strongly interact with each other.

The physicists still do not have much clue about NFL, which makes it very difficult to make concrete predictions. Still, these systems are essential for the continued prosperity of human society, as NFLs hold the key in making use of high-temperature superconducting material that will solve the energy crisis. Currently, the so-called high-temperature superconducting materials still only work at temperature scale of-100 Celsius - they are called high-temperature in comparison with the FL superconductors, which work at temperature scale of -200 Celsius - so it is still hard to put high-temperature superconductors into daily usage at room temperature, but only then can we enjoy the nice properties of such material that the electronic power will not be loss in heat due to resistivity. Only when we understand how the NFL in high-temperature superconductor works at -100 Celsius, can we then design the ultimate material to work at room temperature. Therefore, the complete understanding of NFL is of vital importance.

Physicists from analytical background have been trying to understand NFL for about half a century. The problem of analytical calculation is that, due to the quantum many-body nature of the NFL, the convergence and accuracy of many theoretical predictions cannot be controlled or guaranteed; one would need unbiased quantum computation to verify these prepositions.

At the numerical front, there have been many previous attempts, but the problem is that the results obtained are always different from the analytical prediction. For example, the most important quantity of the NFL, the self-energy Σ , which describes the level of the electron interactions in the material, is expected to have a power-law frequency dependence such as Σ~ω2/3in the model exhibited in Fig.1. However, the computed self-energy doesn’t follow such as power-law, it shows a slow diverging behaviour, that is the self-energy computed doesn’t go to zero as frequency is reduced, but instead gets larger and large, as the data in Fig.2 (b) indicated. Such difference makes the situation even more perplexing.

After a very inspirational discussion between Dr Meng, Professor Chubukov, and Dr Klein, they realized that the setting of the numerical simulation is actually different from that of the analytical calculation. Such subtlety comes from the fact that the model simulations are performed on the finite system at finite temperature, that is T≠0, whereas the analytical expectations are strictly at the zero temperature T=0. In other words, the numerical data actually contain both the zero temperature NFL contribution and the contribution from the fluctuations at finite temperature. To be able to reveal the NFL behaviour from the lattice model simulation such as the setting in Fig.1, one would need to deduce the finite temperature contribution.

This turns out to be the key revelation to the puzzle of NFL. Dr Klein, Dr Sun and Prof Chubukov derived the analytical form of the finite temperature contribution (with the input from the lattice model in Fig.1 designed by Dr Meng and Dr Xu) for Dr Meng and Dr Xu to employ and deduce from the numerical data, the results are shown as the black dashed line and the data round it in Fig. 2(c). To everyone’s surprise and ecstasy, the results after the deduction perfectly exhibit the expected NFL behaviour, from finite temperature all the way to zero temperature, the power-law is revealed. It is the first time that such clear NFL behaviour has been obtained from unbiased numerical simulation.

Dr Meng said it is expected that this work will inspire many follow-up theoretical and experimental researches, and in fact, promising results for further identification of NFL behaviour in another model system have been obtained by the further investigations, he said: “This research work reveals the puzzle of Non-Fermi-liquid for several decades and paves the avenue for the establishment of new paradigm of quantum metals beyond those more than half-a-century ago. Eventually, we will be able to understand the NFL materials such as high-temperature superconductors as we understand simple metals such as Cooper and Sliver now, and such new understanding will solve the energy crisis and bring better industrial and personal applications to the society.”

Link of the journal paper: https://www.nature.com/articles/s41535-020-00266-6

Source: https://www.hku.hk/press/news_detail_21752.html

Note 1: Lev Landau is a Soviet physicist and among the founders of condensed matter physics. Enrico Fermi is an American-Italian physicist and one of the creators of the quantum mechanics.

]]>DQMC Note 2：从Hubbard Model开始的DQMC

DQMC Note 5：Checkerboard分解、Self-learning

夫人之相与，俯仰一世，或取诸怀抱，

悟言一室之内；或因寄所托，放浪形骸之外。

虽趣舍万殊，静躁不同，当其欣于所遇，

暂得于己，快然自足，不知老之将至。

——王羲之《兰亭集序》

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Quantum materials are becoming the cornerstone for the continuous prosperity of human society. From the next-generation AI computing chips that go beyond Moore’s law (the law is the observation that the number of transistors in a dense integrated circuit doubles about every two years, our PC and smartphone are all based on the success of it. Nevertheless, as the size of the transistors are becoming smaller to the scale of nanometer, the behaviour of electrons are subject to quantum mechanics, the Moore’s law is expecting to breakdown very soon), to the high speed Maglev train and the topological unit for quantum computers, investigations along these directions all belong to the arena of quantum material research.

However, such research is by no means easy, the difficulty lies in the fact that scientists have to solve the millions of thousands of the electrons in the material in a quantum mechanical way (hence quantum materials are also called quantum many-body systems), this is far beyond the time of paper and pencil, and requires instead modern quantum many-body computational techniques and advanced analysis. Thanks to the fast development of the supercomputing platforms all over the world, scientists and engineers are now making great use of these computation facilities and advanced mathematical tools to discover better materials to benefit our society.

The research is inspired by the KT phase theory avocated by J Michael Kosterlitz, David J Thouless and F Duncan M Haldane, laureates of the Nobel Prize in Phyiscs 2016. They were awarded for their theoretical discoveries of topological phase and phase transitions of matter. Topology is a new way of classifying and predicting the properties of materials in condensed matter physics, and is now becoming the main stream of quantum material research and industry, with broad potential applications in quantum computer, lossless transmission of signals for information technology, etc. Back to 1970s, Kosterlitz and Thouless had predicted the existence of topological phase, hence named after them as the KT phase, in quantum magnetic materials. However, although such phenomena have been found in superfluids and superconductors, KT phase has yet been realized in bulk magnetic material.

The joint team is led by Dr Zi Yang Meng from HKU, Dr Wei Li from Beihang Univeristy and Professor Yang Qi from Fudan University. Their joint effort has revealed the comprehensive properties of the material TMGO. For example, in Figure 2 (see below), by self-adjustable tensor network calculation, they computed the properties of the model system at different temperature, magnetic field, and by comparing with the corresponding experimental results of the material, they identify the correct microscopic model parameters. With the correct microscopic model at hand, they then performed quantum Monte Carlo simulation and obtained the neutron scattering magnetic spectra at different temperatures (neutron scattering is the established detection method for material structure and their magnetic properties, the closest such facility to Hong Kong is the China Spallation Neutron Source in Dongguan, Guangdong). As shown in Figure 3 (see below), the magnetic spectra with its unique signature at the M point is the dynamical fingerprint of the topological KT phase that has been proposed more than half-a-century ago.

“This research work provides the missing piece of topological KT phenomena in the bulk magnetic materials, and has completed the half-a-century pursuit which eventually leads to the Nobel Physics Prize of 2016. Since the topological phase of matter is the main theme of condensed matter and quantum material research nowadays, it is expected that this work will inspire many follow-up theoretical and experimental researches, and in fact, promising results for further identification of the topological properties in quantum magnet have been obtained among the joint team and our collaborators,” said Dr Meng.

Dr Meng added: “The joint team research across Hong Kong, Beijing and Shanghai, also sets up the protocol of modern quantum material research, such protocol will certainly lead to more profound and impactful discoveries in quantum materials. The computation power of our smartphone nowadays is more powerful than the supercomputers 20 years ago, one can optimistically foresee that with the correct quantum material as the building block, the personal devices in 20 years can certainly be more powerful than the fastest supercomputers right now, with minimal energy cost of everyday battery.”

Link of journal paper: https://www.nature.com/articles/s41467-020-14907-8

HKU Press Releases: https://www.hku.hk/press/press-releases/detail/21179.html

]]>Superconductivity, in which electrons pass through a material without resistance, was an important experimental discovery in the early 1900s because it holds great potential for better energy transportation and materials science. However, the ultra-cold temperature required – initially about -200 degrees Celsius – was for many years an obstacle to these developments. In the 1980s, scientists discovered new materials that exhibit superconductivity at temperatures around -100 degrees Celsius. This “high-temperature” superconductivity is considered one of the greatest success in modern quantum materials, but until recently it was not really understood why this “high-temperature” superconductivity occurred. This lack of understanding has hindered further advances both in the quantum many-body theory and materials realisations. The key of understanding the high-temperature superconductors, lies in the modeling and understanding the metallic states in which electrons are interacted in a quantum many-body manner, from which the superconductivity emerges.

Now, new work by Dr Meng Zi Yang and his collaborators has helped to fill in some of the blanks about the quantum critical metals from which the high-temperature superconductors emerge. The key lies in a proper modelling and an unbiased solution of the model that gives rise to the understanding the metallic states in which electrons interact in a quantum many-body manner.

The scholars designed a lattice model of interacting electrons and solved it with state-of-art quantum computation platforms – the Tianhe supercomputer in China’s national supercomputer centre.

Their goal was to understand the behaviour of interacting electrons in metal, especially close to a critical point in the transition between magnetic metal and non-magnetic metal. This was not possible using traditional simple analytical methods (such as mean-field treatments) because of the scale involved – quantum fluctuations have to be observed among a huge number of electrons (at 10²³).

Dr Meng brought in computational expertise to the problem, which involved applying a quantum Monte Carlo method – essentially, gambling where an electron sits in the system according to the fundamental principles of quantum mechanics – to engineer the transition of a magnetic metal to a non-magnetic metal. The team then used the Tianhe supercomputer to solve the problem.

“The magic happens when there is a transition from magnetic metal to non-magnetic metal because the interaction between electrons is strongest at that point and it is here where interesting phenomena such as critical metal and eventually superconductivity is generated,” Dr Meng said.

This kind of quantum critical metallic state has not been solved in an unbiased manner in research before and it gives scientists a new way of understanding the parent state of high-temperature superconductivity, with major implications for both quantum many-body theories and future efficient energy transportation.

Liu Z.H., Pan G., Xu X.Y., Sun K. and Meng Z.Y., "Itinerant quantum critical point with fermion pockets and hotspots", Proceedings of the National Academy of Sciences of the USA (PNAS), 2019, 116 (34), 16760-16767.

HKU Research Stories: https://www.hku.hk/research/stories/20645/

]]>很多年前，大概是还觉得《读者》之类的鸡汤文字集合是文学的时候吧，不知在什么地方见到过以此为题目的一本书。内容自然记不清楚了，大抵都是些content-free 的大实话：人生艰难，痛苦总是多于欢欣，没有爱的扶持我们怎么能够坚持下去云云。时过境迁，已经练就了铁石心肠鸡汤不入，只有这个题目还映在脑海里。Continue reading

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