Field theories for condensed matter

An important trend in the condensed matter physics of the last two decades, has been the use of advanced quantum field theoretical methods to discuss various subtle and fundamental properties of interacting many-particle systems at low temperatures. There are several reasons for this trend. The first reason is of course that a traditional topic in condensed matter physics (and statistical physics) is the study of phase transitions and critical phenomena, for which the universal properties are independent of the microscopic details of the system and can therefore be determined by a quantum field theory describing only the large-scale properties of the system of interest. Since the latter are usually solely determined by symmetry considerations, this has lead to the important concept of spontaneous symmetry breaking which has turned out to be not only highly successful in condensed matter physics but also in high-energy physics and in particular ``the Standard Model'' of elementary particles. The symmetry-breaking concept also allows for a very natural description of topological defects in a medium where symmetry breaking does occur.

A second reason is that soon after the development of the renormalization group methods for critical phenomena, it was realized that the same methods can in fact be used to describe the large-scale properties of many-particle systems at any temperature and not only near the critical one. Moreover, application of the renormalization group ideas does not only lead to an understanding of the static behaviour but also of the dynamical properties. These features have in recent years led to the study of so-called quantum phase transitions. This active field of research is anticipated to become even more important in the next five to ten years.

The importance of field-theoretical methods in condensed matter physics is also associated with the observation that also the effects of impurities, i.e. disorder, can be treated in this way. Apart from the technological importance of disorder, e.g. for superconducting magnets, disorder leads also to fundamentally new physics such as the phenomenon of localization and the quantum Hall effect.

The fractional quantum Hall effect: renormalization group flow of the transversal and longitudinal conductances, with the stable fixed point values on the horizontal axis characterizing the 'Hall plateaus'.

The quantum Hall effect

An important direction that is pursued at the ITFA (Pruisken, Schoutens) is the study of the quantum Hall effect for a two-dimensional electron gas in a (high) magnetic field. This topic is particularly rich in applications of advanced quantum field theoretical methods and it offers an exciting testing ground where field theory predictions can be confronted with laboratory data. The scaling theory for the quantum Hall plateau transitions has been a prime example in this respect. This topic, and related issues in the quantum theory of transport, continue to attract the attention of both theoretical and experimental groups worldwide. The fractional quantum Hall effect is a beautiful laboratory system for the physics of particles with fractional charge and statistics. The use of topological field theories (Chern-Simons theory) has proven to be highly successful and has led to a theory of the quantum Hall effect in terms of edge states that form a chiral Luttinger liquid. Important in this respect are experiments where electrons are allowed to tunnel between two quantum Hall edges. A recent development has been the observation (both theoretical and experimental) that under certain conditions the elementary excitations of the two-dimensional electron gas are spin-textures called skyrmions. A final issue is the nature of the quantum Hall states in the so-called second Landau level, an example being a quantum Hall state observed at filling fraction . It has been proposed that these states fall into the category of `non-abelian quantum Hall states' and hence provide a laboratory realization of the phenomenon of non-abelian statistics.

The research groups of Pruisken and Schoutens work on all theoretical issues listed in the above. In addition, they are extending a collaboration with experimentalist from the Van der Waals - Zeeman Institute (De Visser in particular).

Many body effects in radiation and matter

As part of another collaboration with the Van der Waals - Zeeman Institute one studies the theory of quantized fields in dielectrics. The quantization scheme for the radiation field in a dielectric becomes non-trivial if non-uniformities and dispersion effects are taken into account. These effects are intimately connected to the absorptive behaviour in the medium. Quantization in an absorptive environment has to proceed by introducing stochastic Langevin terms in the field sources. The ensuing formalism is relevant for the description of molecular emission and absorption in dielectrics. Suppression or enhancement of emission processes by manipulating the environment is currently an active subject of research in quantum optics, both theoretically and experimentally (cavity quantum electrodynamics, photonic crystals etc.).
Another research branch here concerns the study of strongly coupled plasmas. In the framework of a project of the FOM statistical physics division research is focused on boundary effects in field theories describing dense systems of charged particles. In the coming years we are planning to continue our research on the influence of boundaries on the fluctuation and correlation properties of magnetized dense plasmas. Topics will be: sum rules, asymptotic behaviour of equal-time and time-displaced correlation functions, magnetic induction effects, radiation field corrections.

Dynamics in superfluid ³He

While effective field theoretic descriptions of the equilibrium properties of quantum fluids like ³He have received considerable attention (Nobel prize 1996), surprisingly little effort has been devoted to time-dependent aspects of symmetry breaking phase transitions like the superfluid transition. A model of weakly interacting fermionic gases is a good description of atomic gases in magnetic traps, such as are used for the recent experimental realizations of Bose-Einstein condensation, but it has proven to be qualitatively adequate also for superfluid ³He.

An interesting development which in part motivates the research at the ITFA (van Weert) concerns the quench experiments by the Helsinki low-temperature group. In these experiments it was observed that the rapid cooling of the locally overheated ³He liquid through the superfluid phase transition results in the formation of vortex rings. It has been suggested that these experiments test different theories of cosmological defect formation at a stage of the expanding universe. While thus the physics of the early universe may be modeled in the laboratory, where cooling rates can be controlled, it requires a consistent treatment of time dependent mean fields, both to verify the accuracy of the model and to make further predictions.