FOR 2316:  Correlations in Integrable Quantum Many-Body Systems

• Subject Area: Physics
• Term: since 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 267822229

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. We intend to address features arising in the continuum limit of integrable lattice models, e.g. modified non-linear Tomonaga-Luttinger liquids, conformal field theories with extended symmetries and logarithmic conformal field theories. In each of these areas, with strong interest to large communities, many fundamental questions are still open.There is 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 applicants have gathered strong expertise in the study of solvable model systems. The coordination of our expertise bears the prospect of obtaining 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 the applicants. This is where the coordinated research of the applicants will produce genuinely new results.

• DFG Programme: Research Units
• International Connection: Canada, France, Japan

Projects

• Coordination Funds (Applicant Kluemper, Andreas )
• Correlation functions of integrable lattice models and quantum field theories (Applicant Boos, Hermann )
• Dynamical correlation functions of integrable quantum systems (Applicant Karbach, Michael )
• Dynamical correlation functions of the XXZ model at finite temperatures (Applicants Göhmann, Frank ;  Karbach, Michael )
• Efficient thermodynamics for strongly correlated fermions and bosons (Applicant Kluemper, Andreas )
• Equal-time correlation functions of integrable lattice models (Applicants Boos, Hermann ;  Göhmann, Frank )
• Impurities and disorder in nearly integrable models (Applicant Schneider, Imke )
• LATTICE APPROACH TO INTEGRABLE QUANTUM FIELD THEORIES AND APPLICATIONS (Applicant Boos, Hermann )
• Non-Abelian anyons (Applicant Frahm, Holger )
• Relaxation dynamics following a quench in integrable and almost integrable quantum chains (Applicant Sirker, Jesko )
• Spin chains and vertex models based on superalgebras (Applicant Frahm, Holger )
• Transport properties of integrable quantum systems (Applicant Kluemper, Andreas )

• Spokesperson: Professor Dr. Andreas Kluemper