Strongly correlated systems

Introduction

Strongly correlated systems are a class of physical systems, typically described by quantum mechanics, where the behavior of the system cannot be described in terms of the behavior of its individual constituents. This is due to the strong interactions between the particles, leading to a high degree of correlation in their behavior. These systems are of great interest in condensed matter physics, as they exhibit a wide range of fascinating phenomena, such as high-temperature superconductivity, quantum phase transitions, and the fractional quantum Hall effect.

Theoretical Background

In a strongly correlated system, the interactions between particles are so strong that they cannot be treated as small perturbations on a system of non-interacting particles. This is in contrast to weakly correlated systems, where the interactions can be treated as a small perturbation on a system of non-interacting particles. In a strongly correlated system, the behavior of the system as a whole is not simply the sum of the behaviors of its individual constituents. Instead, the system exhibits emergent behavior, where new phenomena arise that are not present in the individual constituents.

The theoretical description of strongly correlated systems is a challenging problem in condensed matter physics. Traditional methods, such as mean-field theory and perturbation theory, are not applicable due to the strong interactions. Instead, novel theoretical approaches are required, such as the use of quantum field theory, the renormalization group, and numerical methods like quantum Monte Carlo simulations.

Experimental Observations

Strongly correlated systems are found in a wide range of materials, including transition metal oxides, heavy fermion compounds, and high-temperature superconductors. These materials exhibit a wide range of fascinating phenomena, such as unconventional superconductivity, quantum phase transitions, and the fractional quantum Hall effect.

In the case of high-temperature superconductors, for example, the strong correlations between the electrons lead to a state of matter where electrical resistance vanishes below a certain temperature. This phenomenon, known as superconductivity, was first discovered in mercury by Heike Kamerlingh Onnes in 1911. However, the mechanism behind high-temperature superconductivity, which occurs in certain copper-oxide materials at temperatures much higher than those of traditional superconductors, is still not fully understood and is the subject of ongoing research.

Close-up image of a high-temperature superconductor material.

Close-up image of a high-temperature superconductor material.

Future Directions

The study of strongly correlated systems is a vibrant field of research, with many open questions and exciting future directions. One of the key challenges is to develop a theoretical understanding of these systems that can predict their behavior and guide the search for new materials with desirable properties.

In addition, the development of new experimental techniques, such as angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM), is providing unprecedented insights into the behavior of strongly correlated systems. These techniques allow researchers to probe the electronic structure of these materials with high spatial and energy resolution, revealing new aspects of their behavior.

Another exciting direction is the exploration of strongly correlated systems in the context of quantum information science. There is growing interest in using these systems as platforms for quantum computation and quantum simulation, due to their rich quantum mechanical behavior and the potential for strong quantum entanglement.

See Also

• Quantum Phase Transition
• High-Temperature Superconductivity
• Quantum Field Theory