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The auxiliary field quantum Monte Carlo (AFQMC) method has been a workhorse in the field of strongly correlated electrons for a long time and has found its most recent implementation in the ALF package (alf.physik.uni-wuerzburg.de). The utilization of the Trotter decomposition to decouple the interaction from the non-interacting Hamiltonian makes this method inherently second order in terms of the imaginary time slice. We show that due to the use of the Hubbard-Stratonovich transformation (HST) a semigroup structure on the time evolution is imposed that necessitates the introduction of a new family of complex-hermitian splitting methods for the purpose of reaching higher order. We will give examples of these new methods and study their efficiency, as well as perform comparisons with other established second and higher order methods in the realm of the AFQMC method.

The term Research Software Engineer, or RSE, emerged a little over 10 years ago as a way to represent individuals working in the research community but focusing on software development. The term has been widely adopted and there are a number of high-level definitions of what an RSE is. However, the roles of RSEs vary depending on the institutional context they work in. At one end of the spectrum, RSE roles may look similar to a traditional research role. At the other extreme, they resemble that of a software engineer in industry. Most RSE roles inhabit the space between these two extremes. Therefore, providing a straightforward, comprehensive definition of what an RSE does and what experience, skills and competencies are required to become one is challenging. In this community paper we define the broad notion of what an RSE is, explore the different types of work they undertake, and define a list of foundational competencies as well as values that outline the general profile of an RSE. These foundational skills are encountered to a large extent within the skill sets of current RSEs in Germany and beyond, and we propose them as a starting point for aspiring RSEs to shape their technical profile. Further research and training can build upon this foundation of skills and focus on various aspects in greater detail. We expect that graduates and practitioners will have a larger and more diverse set of skills than outlined here. On this basis, we elaborate on the progression of these skills along different dimensions. We look at specific types of RSE roles, propose recommendations for organisations, give examples of future specialisations, and detail how existing curricula fit into this framework.

The term Research Software Engineer, or RSE, emerged a little over 10 years ago as a way to represent individuals working in the research community but focusing on software development. The term has been widely adopted and there are a number of high-level definitions of what an RSE is. However, the roles of RSEs vary depending on the institutional context they work in. At one end of the spectrum, RSE roles may look similar to a traditional research role. At the other extreme, they resemble that of a software engineer in industry. Most RSE roles inhabit the space between these two extremes. Therefore, providing a straightforward, comprehensive definition of what an RSE does and what experience, skills and competencies are required to become one is challenging. In this community paper we define the broad notion of what an RSE is, explore the different types of work they undertake, and define a list of foundational competencies as well as values that outline the general profile of an RSE. Further research and training can build upon this foundation of skills and focus on various aspects in greater detail. We expect that graduates and practitioners will have a larger and more diverse set of skills than outlined here. On this basis, we elaborate on the progression of these skills along different dimensions. We look at specific types of RSE roles, propose recommendations for organisations, give examples of future specialisations, and detail how existing curricula fit into this framework.

Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements and embeds research knowledge, and constitutes an essential research product in itself. Research software must be sustainable in order to understand, replicate, reproduce, and build upon existing research or conduct new research effectively. In other words, software must be available, discoverable, usable, and adaptable to new needs, both now and in the future. Research software therefore requires an environment that supports sustainability. Hence, a change is needed in the way research software development and maintenance are currently motivated, incentivized, funded, structurally and infrastructurally supported, and legally treated. Failing to do so will threaten the quality and validity of research. In this paper, we identify challenges for research software sustainability in Germany and beyond, in terms of motivation, selection, research software engineering personnel, funding, infrastructure, and legal aspects. Besides researchers, we specifically address political and academic decision-makers to increase awareness of the importance and needs of sustainable research software practices. In particular, we recommend strategies and measures to create an environment for sustainable research software, with the ultimate goal to ensure that software-driven research is valid, reproducible and sustainable, and that software is recognized as a first class citizen in research. This paper is the outcome of two workshops run in Germany in 2019, at deRSE19 - the first International Conference of Research Software Engineers in Germany - and a dedicated DFG-supported follow-up workshop in Berlin.

Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements and embeds research knowledge, and constitutes an essential research product in itself. Research software must be sustainable in order to understand, replicate, reproduce, and build upon existing research or conduct new research effectively. In other words, software must be available, discoverable, usable, and adaptable to new needs, both now and in the future. Research software therefore requires an environment that supports sustainability. Hence, a change is needed in the way research software development and maintenance are currently motivated, incentivized, funded, structurally and infrastructurally supported, and legally treated. Failing to do so will threaten the quality and validity of research. In this paper, we identify challenges for research software sustainability in Germany and beyond, in terms of motivation, selection, research software engineering personnel, funding, infrastructure, and legal aspects. Besides researchers, we specifically address political and academic decision-makers to increase awareness of the importance and needs of sustainable research software practices. In particular, we recommend strategies and measures to create an environment for sustainable research software, with the ultimate goal to ensure that software-driven research is valid, reproducible and sustainable, and that software is recognized as a first class citizen in research. This paper is the outcome of two workshops run in Germany in 2019, at deRSE19 - the first International Conference of Research Software Engineers in Germany - and a dedicated DFG-supported follow-up workshop in Berlin.

This thesis deals with quantum Monte Carlo simulations of correlated low dimensional electron systems. The correlation that we have in mind is always given by the Hubbard type electron electron interaction in various settings. To facilitate this task, we develop the necessary methods in the first part. We develop the continuous time interaction expansion quantum algorithm in a manner suitable for the treatment of effective and non-equilibrium problems. In the second part of this thesis we consider various applications of the algorithms. First we examine a correlated one-dimensional chain of electrons that is subject to some form of quench dynamics where we suddenly switch off the Hubbard interaction. We find the light-cone-like Lieb-Robinson bounds and forms of restricted equilibration subject to the conserved quantities. Then we consider a Hubbard chain subject to Rashba spin-orbit coupling in thermal equilibrium. This system could very well be realized on a surface with the help of metallic adatoms. We find that we can analytically connect the given model to a model without spin-orbit coupling. This link enabled us to interpret various results for the standard Hubbard model, such as the single-particle spectra, now in the context of the Hubbard model with Rashba spin-orbit interaction. And finally we have considered a magnetic impurity in a host consisting of a topological insulator. We find that the impurity still exhibits the same features as known from the single impurity Anderson model. Additionally we study the effects of the impurity in the bath and we find that in the parameter regime where the Kondo singlet is formed the edge state of the topological insulator is rerouted around the impurity.

The auxiliary field quantum Monte Carlo (AFQMC) method has been a workhorse in the field of strongly correlated electrons for a long time and has found its most recent implementation in the ALF package (https://alf.physik.uni-wuerzburg.de). The utilization of the Trotter decomposition to decouple the interaction from the non-interacting Hamiltonian makes this method inherently second order in terms of the imaginary time slice. We show that due to the use of the Hubbard-Stratonovich transformation (HST) a semigroup structure on the time evolution is imposed that necessitates the introduction of a new family of complex-hermitian splitting methods for the purpose of reaching higher order. We will give examples of these new methods and study their efficiency, as well as perform comparisons with other established second and higher order methods in the realm of the AFQMC method.

We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice \\(t-t'\\) Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publish a set of recommended choices for the functional renormalization group, shown to decrease the computational cost for FRG calculations and representing a valuable basis for further investigations.

We present a numerical quantum Monte Carlo (QMC) method for simulating the 3D phase transition on the recently proposed fuzzy sphere [Phys. Rev. X 13, 021009 (2023)]. By introducing an additional \\(SU(2)\\) layer degree of freedom, we reformulate the model into a form suitable for sign-problem-free QMC simulation. From the finite-size-scaling, we show that this QMC-friendly model undergoes a quantum phase transition belonging to the 3D Ising universality class, and at the critical point we compute the scaling dimensions from the state-operator correspondence, which largely agrees with the prediction from the conformal field theory. These results pave the way to construct sign-problem-free models for QMC simulations on the fuzzy sphere, which could advance the future study on more sophisticated criticalities.

As a new step towards defining complexity for quantum field theories, we map Nielsen operator complexity for \\(SU(N)\\) gates to two-dimensional hydrodynamics. We develop a tractable large \\(N\\) limit that leads to regular geometries on the manifold of unitaries as \\(N\\) is taken to infinity. To achieve this, we introduce a basis of non-commutative plane waves for the \\(\\mathfrak{su}(N)\\) algebra and define a metric with polynomial penalty factors. Through the Euler-Arnold approach we identify incompressible inviscid hydrodynamics on the two-torus as a novel effective theory of large-qudit operator complexity. For large \\(N\\), our cost function captures two essential properties of holographic complexity measures: ergodicity and conjugate points.