Correlations in Integrable Quantum Many-Body Systems

The objects of our daily experience, macroscopic pieces of matter, are composed of a very large number of microscopic constituents, ions and electrons, say. One of the major goals of our science (many-body physics) is to explain quantitatively the material properties of macroscopic matter from the properties of its microscopic constituents. This can be achieved by calculating the correlations of local quantities on the microscopic side. Correlation functions of local operators determine the mechanical, optical and electric properties of matter, which are probed by exerting stress, shining light or applying a voltage.

Correlation functions are notoriously hard to calculate. Typically one or the other type of approximation has to be applied. As these approximations are often hard to control, this is the place where fundamental science turns into phenomenology. Exceptions are rare and therefore important. They are the subject of our research project.

The goal of our research group is the development of many-body standard reference systems with known static and dynamical correlation functions at arbitrary temperature, on the lattice and in the continuum, very much like Bosonization provides standard reference systems near T = 0, namely conformal field theories with central charges c = 1 and known static low-temperature properties.

Specifically, we plan to develop further the theory of exact correlation functions of Heisenberg spin chains and their relatives. Parallel to these activities we intend to address features arising in the continuum limit of integrable lattice models, e.g. modified nonlinear Tomonaga-Luttinger liquids, conformal field theories with extended symmetries and logarithmic conformal field theories. In each of these areas, while being of strong topical interest to large communities, many fundamental questions are still open.

There will be a multitude of applications in various fields of theoretical and experimental physics, comprising e.g. exotic transport in solids or the dynamics of ultra-cold quantum gases in traps.

In our individual research we have gathered strong expertise in the study of solvable model systems. The coordination of our expertise will allow us to obtain qualitatively different new results. In recent years, developments took place in the fields of cold atomic gases, quantum information theory, non-equilibrium systems and gauge-string dualities that enabled the identification of core questions which can be answered by techniques developed or yet to be developed by us. This is where we hope that the coordinated research of this research unit will produce genuinely new results.