Physics of Strongly Correlated Systems
Physics of Strongly Correlated Systems
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
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.