Physics of Strongly Correlated Systems

Eugene Demler

The main focus of my research is understanding the properties of systems with strong interactions and correlations between the constituent particles. Here I try to summarize my motivation for working in this field.

Physical systems that we understand well correspond to ensembles of free particles. For example, semiconductors and most metals can be described as having non-interacting electrons. This simple approach is valid because the interaction (Coulomb) energy of electrons is much smaller than their kinetic energy. Another example is alkali atoms, that Bose condense at low temperatures. Alkali atoms can be treated as non-interacting bosons because their scattering length (i.e. the length at which they interact with each other) is much smaller than the average distance between the particles.

However there are important systems for which interactions between the particles are not weak, and these interactions play a major role in determining the properties of such systems. Below I provide several examples of such "strongly correlated systems".

1. Conventional superconductors. Coulomb interaction between electrons and ions in these materials results in a new ground state that can support a dissipationless flow of electrical current.

2. High-temperature superconductors. The transition temperature for these materials is surprisingly high. The origin of superconductivity is still unclear, but it is commonly believed that it comes mostly from the Coulomb interaction between the electrons, rather than the electron-ion interactions that are important for the conventional superconductors. What is also intriguing about the high Tc cuprates is that superconductivity appears in materials that are not good metals to begin with. In fact their normal state properties are so unusual that they are often called "strange metals".

3. Magnetic systems. Coulomb interaction between electrons may lead to a variety of spin ordering patterns, including ferromagnetism (spins of all the particles are alligned), antiferromagnetism (spins of the neighboring particles are antialigned).

4. Quantum Hall systems. In the presense of a strong perpendicular magnetic field electrons confined in one or several two-dimensional layers form a new quantum liquid state, that may have such unusual properties as fractionally charged excitations or uncertain layer index.

5. One dimensional electron systems. Electrons carry two important quantum numbers: charge and spin. When a single electron moves in a vacuum or in a conventional insulator we can observe charge and spin propogating together. By contrast in one dimensional systems interacting electrons disintegrate into charge and spin solitons that propogate at different velocities.

6. The insulating state of bosonic atoms in a periodic potential (optical lattices). At low temperatures we expect Bose particles to condense: most of the particles can be found in a state of zero momentum which helps to minimize their kinetic energy. Such condensation, however, is unfavorable from the point of view of repulsive interactions. Putting atoms in a periodic potential enhances the effective interaction between the particles and one can observe a phase transition from the superfluid state to the insulating state of particles localized around minima of the potential.

At this point we do not have a good general approach for understanding "strongly correlated systems". We know certain aspects of several systems, such as certain quantum Hall systems or some magnetic materials. But we understand very poorly most of the others. For example, the nature of high temperature superconductors remains mysterious in spite of many years of intensive work. Most importantly we do not have a unified view on the systems for which interactions are important. The main goal of my research is to establish a common framework for understanding the physics of strongly correlated systems and to develop general tools for studying the role of interactions in fermionic and bosonic systems. I do it in the context of particular systems, such as high temperature superconductors, quantum magnets, or quantum Hall systems, but I concentrate on general and universal features of the interactions.

Many systems that I am thinking about have a promising future for applications in industry. High temperature superconductors are already used for efficient energy transmission and for constructing new types of electronic devices. Magnetic materials are important for memory devices. Quantum Hall systems and bosonic atoms in optical lattices may be useful for quantum computations and communications. However, I am more intrigued by trying to understand how the nature works than by finding useful applications of new materials.