ERC FUNDED PROJECTS

Some of the most fascinating physical phenomena are experimentally observed in strongly correlated electron systems and, on the theoretical side, only poorly understood hitherto. The aim of the ERC project AbinitioDGA is the development, implementation and application of a new, 21th century method for the ab initio calculation of materials with such strong electronic correlations. AbinitioDGA includes strong electronic correlations on all time and length scales and hence is a big step beyond the state-of-the-art methods, such as the local density approximation, dynamical mean field theory, and the GW approach (Green function G times screened interaction W). It has the potential for an extraordinary high impact not only in the field of computational materials science but also for a better understanding of quantum critical heavy fermion systems, high-temperature superconductors, and transport through nano- and heterostructures. These four physical problems and related materials will be studied within the ERC project, besides the methodological development. On the technical side, AbinitioDGA realizes Hedin's idea to include vertex corrections beyond the GW approximation. All vertex corrections which can be traced back to a fully irreducible local vertex and the bare non-local Coulomb interaction are included. This way, AbinitioDGA does not only contain the GW physics of screened exchange and the strong local correlations of dynamical mean field theory but also non-local correlations beyond on all length scales. Through the latter, AbinitioDGA can prospectively describe phenomena such as quantum criticality, spin-fluctuation mediated superconductivity, and weak localization corrections to the conductivity. Nonetheless, the computational effort is still manageable even for realistic materials calculations, making the considerable effort to implement AbinitioDGA worthwhile.

1 491 090 €

Start date: 2013-01-01, End date: 2018-07-31

Real-world optimization problems pose major challenges to algorithmic research. For instance, (i) many important problems are believed to be intractable (i.e. NP-hard) and (ii) with the growth of data size, modern applications often require a decision making under {\em incomplete and dynamically changing input data}. After several decades of research, central problems in these domains have remained poorly understood (e.g. Is there an asymptotically most efficient binary search trees?) Existing algorithmic techniques either reach their limitation or are inherently tailored to special cases. This project attempts to untangle this gap in the state of the art and seeks new interplay across multiple areas of algorithms, such as approximation algorithms, online algorithms, fixed-parameter tractable (FPT) algorithms, exponential time algorithms, and data structures. We propose new directions from the {\em structural perspectives} that connect the aforementioned algorithmic problems to basic questions in combinatorics. Our approaches fall into one of the three broad schemes: (i) new structural theory, (ii) intermediate problems, and (iii) transfer of techniques. These directions partially build on the PI's successes in resolving more than ten classical problems in this context. Resolving the proposed problems will likely revolutionize our understanding about algorithms and data structures and potentially unify techniques in multiple algorithmic regimes. Any progress is, in fact, already a significant contribution to the algorithms community. We suggest concrete intermediate goals that are of independent interest and have lower risks, so they are suitable for Ph.D students.

1 411 258 €

Start date: 2018-02-01, End date: 2024-01-31

This project aims to develop a universal approach to angular momentum in quantum many-body systems based on the angulon quasiparticle recently discovered by the PI. We will establish a general theory of angulons in and out of equilibrium, and apply it to a variety of experimentally studied problems, ranging from chemical dynamics in solvents to solid-state systems (e.g. angular momentum transfer in the Einstein-de Haas effect and ultrafast magnetism). The concept of angular momentum is ubiquitous across physics, whether one deals with nuclear collisions, chemical reactions, or formation of galaxies. In the microscopic world, quantum rotations are described by non-commuting operators. This makes the angular momentum theory extremely involved, even for systems consisting of only a few interacting particles, such as gas-phase atoms or molecules. Furthermore, in most experiments the behavior of quantum particles is inevitably altered by a many-body environment of some kind. For example, molecular rotation – and therefore reactivity – depends on the presence of a solvent, electronic angular momentum in solids is coupled to lattice phonons, highly excited atomic levels can be perturbed by a surrounding ultracold gas. If approached in a brute-force fashion, understanding angular momentum in such systems is an impossible task, since a macroscopic number of particles is involved. Recently, the PI and his team have shown that this challenge can be met by introducing a new quasiparticle – the angulon. In 2017, the PI has demonstrated the existence of angulons by comparing his theory with 20 years of measurements on molecules rotating in superfluids. Most importantly, the angulon concept allows one to gain analytical insights inaccessible to the state-of-the-art techniques of condensed matter and chemical physics. The angulon approach holds the promise of opening up a new interdisciplinary research area with applications reaching far beyond what is proposed here.

1 499 588 €

Start date: 2019-02-01, End date: 2024-01-31

AQSuS aims at experimentally implementing analogue quantum simulation of interacting spin models in two-dimensional geometries. The proposed experimental approach paves the way to investigate a broad range of currently inaccessible quantum phenomena, for which existing analytical and numerical methods reach their limitations. Developing precisely controlled interacting quantum systems in 2D is an important current goal well beyond the field of quantum simulation and has applications in e.g. solid state physics, computing and metrology. To access these models, I propose to develop a novel circuit quantum-electrodynamics (cQED) platform based on the 3D transmon qubit architecture. This platform utilizes the highly engineerable properties and long coherence times of these qubits. A central novel idea behind AQSuS is to exploit the spatial dependence of the naturally occurring dipolar interactions between the qubits to engineer the desired spin-spin interactions. This approach avoids the complicated wiring, typical for other cQED experiments and reduces the complexity of the experimental setup. The scheme is therefore directly scalable to larger systems. The experimental goals are: 1) Demonstrate analogue quantum simulation of an interacting spin system in 1D & 2D. 2) Establish methods to precisely initialize the state of the system, control the interactions and readout single qubit states and multi-qubit correlations. 3) Investigate unobserved quantum phenomena on 2D geometries e.g. kagome and triangular lattices. 4) Study open system dynamics with interacting spin systems. AQSuS builds on my backgrounds in both superconducting qubits and quantum simulation with trapped-ions. With theory collaborators my young research group and I have recently published an article in PRB [9] describing and analysing the proposed platform. The ERC starting grant would allow me to open a big new research direction and capitalize on the foundations established over the last two years.

1 498 515 €

Start date: 2017-04-01, End date: 2022-03-31