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Stepped wedge cluster randomized experiments (SW-CREs) represent a class of unidirectional crossover designs. Although SW-CREs have become popular, definitions of estimands and robust methods to target estimands under the potential outcomes…
Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…
We study spin density wave quantum critical points in two dimensional metals with a quenched disorder potential coupling to the electron density. Adopting an $\epsilon$-expansion around three spatial dimensions, where both disorder and the…
The topological patterns exhibited by many real-world networks motivate the development of topology-based methods for assessing the similarity of networks. However, extracting topological structure is difficult, especially for large and…
Problems involving disordered systems are usually analyzed for systems with random disorder. However, there are many systems in which the main disorder involves clusters with correlated differences between their properties and those of the…
This work introduces various approaches to include connected three-body terms in unitary many-body theories, focusing a representative example on the driven similarity renormalization group (DSRG). Starting from the least approximate method…
This paper demonstrates that a computer aided perturbation theory can easily be realized by use of a cumulant approach. In contrast to a recent alternative formulation on the basis of Wegner's flow equation method the present approach can…
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the…
Electron Wigner solids (WSs)1-12 provide an ideal system for understanding the competing effects of electron-electron and electron-disorder interactions, a central unsolved problem in condensed matter physics. Progress in this topic has…
We have carried out a theoretical analysis of the Landau-Ginzburg-Wilson effective field theory of a classical incommensurate CDW in the presence of weak quenched disorder. While the possibility a sharp phase transition and long-range CDW…
The perfect quenching of spin tunneling that has previously been discussed in terms of interfering instantons, and has recently been observed in the magnetic molecule \Fe8, is treated using a discrete phase integral (or…
The generalized rotating-wave approximation (GRWA) is presented for the two-qubit and cavity coipling system . The analytical expressions in the zeroth order approximation recover the previous adiabatic ones. The counterrotating-wave terms…
We present a combinatorial model for cluster algebras of type $D_n$ in terms of centrally symmetric pseudotriangulations of a regular $2n$-gon with a small disk in the centre. This model provides convenient and uniform interpretations for…
Throughout this thesis, we investigate how effective field theories, combined with unitarization techniques, can be used to explore physics beyond the Standard Model, with particular emphasis on the dynamical origin of electroweak symmetry…
A new approximate scheme, DSUB$m$, is described for the coupled cluster method. We then apply it to two well-studied (spin-1/2 Heisenberg antiferromagnet) spin-lattice models, namely: the $XXZ$ and the $XY$ models on the square lattice in…
We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then,…
Time Series Clustering is an important subroutine in many higher-level data mining analyses, including data editing for classifiers, summarization, and outlier detection. It is well known that for similarity search the superiority of…
We investigate the charge- and spin dynamical structure factors for the 2D one-band Hubbard model in the strong coupling regime within an extension of the Dynamical Cluster Approximation (DCA) to two-particle response functions. The full…
Stepped wedge designs (SWDs) are increasingly used to evaluate longitudinal cluster-level interventions but pose substantial challenges for valid inference. Because crossover times are randomized, intervention effects are intrinsically…
In this work, we combine the many-body formulation of the internally contracted multireference coupled cluster (ic-MRCC) method with Evangelista's multireference formulation of the driven similarity renormalization group (DSRG). The DSRG…