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Projects
| Large-scale numerical simulations of quantum matterAndreas LäuchliThe proposed project will develop, implement and employ large-scale numerical simulation techniques to investigate various new states of quantum matter. Three different physical systems will be studied: in part i) we will explore phase diagrams, state preparation schemes and the non-equilibrium dynamics of experimentally relevant many body systems - such as atoms and molecules - which are exposed to artificial gauge fields, and which might realize Chern insulators, fractional quantum Hall states, fractional topological insulating states or even currently unknown states of matter. In part ii) we will study SU(N) symmetric spin and Hubbard models at zero and finite temperature in order to explore the possibilities for exotic magnetic ordering or quantum spin liquids in alkaline-earth fermionic atoms confined to optical lattices. Finally, in part iii) we will investigate simulation techniques for many body systems with (engineered) dissipation using matrix product operator (MPO) and quantum jump techniques to address questions such as dynamical phase transitions, steady state properties and real-time dynamics. These algorithms can then also be used to study transport problems through correlated nanostructures occurring in condensed matter systems. For all these physical systems, established powerful approaches such as Exact Diagonalization and the Density Matrix Renormalization Group will be used in the beginning to study large quasi-one-dimensional and small two-dimensional systems, while tensor network approaches such as iPEPS will be implemented and made to scale in order to simulate large two-dimensional systems. | Supporting Organizations |
