One of the central goals in physics is to understand the emergent properties in systems made of many strongly interacting quantum particles. These so-called strongly correlated systems give rise to remarkable phenomena, such as high-temperature superconductivity (HTSC), quantum spin liquids with topological order, and other novel states of matter. In many cases accurate and efficient numerical techniques are indispensable for gaining insight into the properties of these systems. One of the most powerful approaches is Quantum Monte Carlo (QMC), however, it fails for important classes of systems (fermionic and frustrated systems) due to the infamous negative sign problem, which is the main reason why many relevant models are still unsolved. A well-known example is the two-dimensional (2D) Hubbard model which is believed to be relevant for understanding HTSC. Despite immense effort over the last three decades, the Hubbard model and its generalizations are is still not fully solved and a consensus about the mechanism leading to HTSC is still lacking. Thus, to make progress in many-body physics and for the design of future quantum technologies it is essential to develop accurate numerical techniques that go beyond today’s state-of-the-art.
In recent years, groundbreaking progress in the simulation of strongly correlated systems has been achieved with tensor network algorithms, an interdisciplinary field which emerged at the interface between quantum information science and condensed matter physics. A tensor network is a variational ansatz in which a state is efficiently represented by a trace over a product of tensors, where the accuracy can be systematically controlled by the so-called bond dimension D. The best-known example is the matrix product state (MPS) - a very efficient ansatz for quasi-1D systems - which has had an enormous impact on the understanding of low-dimensional systems in the last three decades. Progress in quantum information science has led to the development of tensor networks for 2D systems, such as projected entangled-pair states (PEPS) or the multi-scale entanglement renormalization ansatz (MERA). A particularly powerful ansatz is infinite PEPS (iPEPS) which represents a 2D state directly in the thermodynamic limit, thereby overcoming the problem of finite-size and boundary effects.
Building upon recent breakthroughs with iPEPS, the main goal of this project is to develop and use the next generation of tensor network methods for groundbreaking simulations of challenging open problems in several fields, in order to make major advances in our fundamental understanding of strongly correlated systems. This includes novel powerful algorithms for ground states, time evolution, spectral functions, finite temperature, open systems, and multi-scale approaches, which are used for state-of-the-art simulations of realistic models of HTSC and frustrated materials, and for accurate predictions and benchmarks for experimental quantum simulators of SU(N) and open quantum systems.
