High-Tc Superconductors, Colossal Magnetoresistance

Cold Atom Bose-Einstein Condensation, Optical Lattices

** Emergent Quantum Phenomena**

**一**

Characteristic Energy (K)

Metals, Semiconductors

High-Tc Superconductors, Colossal Magnetoresistance

Quantum Hall Effects, He⁴ Superfluid

Cold Atom Bose-Einstein Condensation, Optical Lattices

At the beginning of the last century, the establishment of relativity and quantum mechanics changed the basic concepts of human understanding of the material world and brought about a scientific revolution. Since then, basic research in physics has developed in two directions in the past century. The first is to develop towards the maximum and minimum, with particle physics and astrocosmology as the core, exploring the most basic units and forces that make up matter, and the basic laws that govern the birth and death of the universe. Great progress has been achieved in the last century progress. The second is to combine quantum mechanics with statistical mechanics to explore the collective movement behavior of complex aggregates composed of a large number of particles. Represented by condensed matter and statistical physics, research in this area has also made great progress with a large number of novel and related quantum phenomena being discovered. It revealed the diversity and complexity of the many-body quantum world, and at the same time it has also exposed our limitations of understanding. More updated physical ideas and methods are expected to be researched.

The hierarchical quantum many-body world has a very rich connotation, in which it is inextricably linked to materials, chemistry, and even biology. The system of dozens of particles may behave very differently from one particle, and the behavior of tens or thousands of particles or dozens of particles may be different, just like changing from a single gold atom to gold. Their behavior cannot be obtained by simply extrapolating the properties of several particles, but instead, new physical phenomena and laws appear at each level. Understanding and manipulating these phenomena and laws is an important content of micro-quantum theoretical research.

In the many-body quantum world, particles are related to each other, and it is because of this interaction that bring about various phenomena such as high temperature superconductivity, quantum Hall effect, and atomic Bose-Einstein condensation. The correlation between particles mainly established in two ways: one is the direct interaction between particles, such as the Coulomb interaction between electrons; the other is the exchange interaction between particles, which is a statistical correlation effect. It does not exist in the system, but it is inevitable in quantum systems.

There are two kinds of particles in nature, one is boson, such as helium 4 atom, and the other is fermion, such as electron. Unlike classic particles, identical bosons and fermions are indistinguishable, and they have very different statistical correlation behaviors. Under certain conditions, just by considering this statistical correlation effect, many extraordinary many-body cooperation phenomena can be obtained. A typical example is the Bose-Einstein condensation of bosons. In the classical system, if a large number of particles are in the same state, it is just a matter of copying the same thing multiple times, and there is no qualitative difference from a few particles in this state. However, when a large number of identical bosons are in the same state (physically called condensation), supercurrent will occur, and many particles will enter a zero-entropy state, resulting in Bose-Einstein condensation. This phenomenon was predicted by Einstein at the beginning of the last century, but direct experimental verification was not realized until the end of the last century.

For fermion system, ignoring the interactions between particles, and just considering their exchange relations, many unexpected results can be obtained. The energy band theory in solid theory is established under this approximation, and has achieved great success. It is an important milestone in the development of solid physics, which gives a unified description of metals, semiconductors, and insulators, laying the physical foundation for modern metal and semiconductor industry. Research in this field continues, but its basic theoretical framework has become very mature in the 1950s. Before that, the conductive behavior of solid materials could only be studied by classical Boltzmann theory, and it was hard to understand why the resistivities of metals, semiconductors, and insulators differed by tens of orders of magnitude.

Obviously, if the interaction between particles and the statistical exchange correlation work at the same time, the resulting physical phenomenon will be more abundant. The electron is a fermion, and any two electrons cannot be in the same state restricted by Pauli exclusion principle. Therefore, the electrons themselves do not condense, but two electrons can be combined together to form a bound state, which has the characteristics of a boson and can also condense. Superconductivity is the result of this cohesion. However, for electrons to form bound states in pairs, they must interact. Therefore, it is not enough to study the superconductivity considering only statistical exchange correlations. In addition to superconductivity, the superfluidity of liquid helium (including helium 3 and helium 4), quantum Hall effect, and Kondo effect are typical examples of quantum correlation effects. The discovery of these phenomena has a certain chance, but each discovery has a huge impact on the study of micro-quantum problems. Strongly correlated physics is to explore the new phenomena and laws caused by the interaction of quantum many-body systems and the statistical correlations and competition.

The study of strong correlation problems began from the early days of quantum theory. The early research focused on superconducting and quantum ferromagnetic problems. One of the important achievements was superconducting BCS theory proposed by three American physicists Bardeen, Cooper, and Schrieffer in 1957. Later the phase transition critical phenomenon further promoted research in this field. However, the real accelerated development and large-scale research were carried out in the 1980s, especially after the discovery of high-temperature superconductors. In the past two decades, five Nobel Prizes in Physics have been awarded to twelve physicists who have made outstanding contributions to the research of strongly correlated physics, demonstrating the status and vitality of this field in physics.

In the research of high-temperature superconductivity, we now have a better understanding of the symmetry of superconductor pairing. However, some of the most basic issues such as the mechanism of superconducting pairing, the roots of the pseudogap and non-Fermi liquid behavior in the normal phase, and the existence of quantum critical phase transition points remain unresolved. The solution of these problems may be of great significance not only for the study of high-temperature superconductors themselves, but also for understanding the ground-state physics of quantum-associated electronic systems such as colossal magnetoresistance that are closely related to Mott insulators.

The quantum Hall effect is a relatively in-depth system, but there are still some basic issues that are not clear, especially some experimental phenomena in the Fractional Quantum Hall effect with an even denominator and in the multilayer quantum Hall system have not been well explained at present. In addition, the oscillation phenomenon of magnetic resistance with the magnetic field under microwave irradiation also needs a clear physical image to explain.

The experiment of Bose-Einstein condensation of cold atoms not only verified Einstein's theoretical prediction, but also promoted the intersection of quantum optics and strongly correlated physics. Using a highly controllable optical grid field to simulate a crystalline material system will become a new research method for studying many-body correlation systems. It has some advantages that traditional solid experimental methods do not have. At present there is not much work in this area, but a promising direction. The Bose-Einstein condensation of excitons has shown a rapid development trend in recent years, and there are many interesting phenomena and problems to be solved.

In the research of heavy fermion materials, antiferromagnetic materials, and other many-body quantum correlation systems, there have been great developments in recent years. In particular, a large number of new materials have been synthesized or discovered. The research on these new materials has revealed some new experimental phenomena and laws, which provided a wealth of physical content for establishing and testing various theoretical models.

Many-body quantum correlation system is the core of condensed matter physics research. Although great progress has been made in this area in recent years, and a large number of quantum phenomena have been discovered, it should be pointed out that these phenomena have been found to be only a small part of the entire connected quantum world. The system needs to be explored and discovered. Even for some of the typical many-body correlation phenomena introduced earlier, our understanding is very limited, especially on the physical reason for these phenomena and the internal relationship between them. At present, it is only possible to deal with each phenomenon individually and study them separately, which lacks a unified theoretical description.

The research and exploration of quantum correlation phenomena has a strong application background in materials, chemistry and other disciplines, and there is a constant connection with these disciplines. In addition, cross-cutting with other disciplines is also increasing. Especially in recent years, with the rapid development of laser cooling technology, the quantum control of polyatomic systems has been realized by applying optical grid fields, which provides a powerful experimental method for the precise manipulation of many-body related systems and promotes the combination of strong related physics and quantum optics. In addition, the research on strong correlation theory has used a lot of knowledge in quantum computation and quantum information theory in recent years. It is found that the method of using quantum entanglement and information entropy to describe a quantum phase change system is much richer than statistical mechanics methods, and has attracted more and more attention.

Strongly related quantum phenomena usually occur in low-dimensional systems, where the interaction between particles and the effects of quantum fluctuations are very strong, which brings great difficulties to research of this aspect. From the perspective of theoretical research, the difficulties mainly come from two aspects: one is that our understanding of the strong correlation is limited, and it lacks a complete and accurate physical image description; the other is the strong correlation system, the interaction is very strong, and cannot be studied by perturbation theory or other mature theoretical methods. The non-perturbative average field approximation requires the existence or approximate existence of a certain long program in the system, and its limitations are also relatively large. Under such circumstances, the study of large-scale numerical simulation and its methods has become increasingly important, occupying an important position in the study of strong correlation theory. The density matrix renormalization group and quantum Monte Carlo method developed in the early 1990's have played an important role in the study of strong correlation problems.

The complexity of the strong correlation also imposes higher requirements on experimental results and experimental techniques. First, the quality of the sample is required higher. In many cases, the preparation of high-quality single crystals is a prerequisite for successful experiments. Only in this way can the uncertain factors caused by impure samples be eliminated. Second, the experimental test methods are also required higher. In addition to the conventional thermodynamic and transport measurements, the test results also are required to have the ability to resolve space, time, energy, and momentum. Therefore, experimental methods such as spatially resolved nuclear magnetic resonance and m-lepton spin resonance, and energy and momentum resolved neutron scattering and angle-resolved photoelectron spectroscopy are widely used in the study of strong correlation problems, and are also emphasized.

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