Related papers: Advanced Mathematical Techniques in Renormalizatio…
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary physics. However, as a direct consequence…
We present a general formalism that allows for the computation of large-order renormalized expansions in the spacetime representation, effectively doubling the numerically attainable perturbation order of renormalized Feynman diagrams. We…
The quantum-field renormalization group method is one of the most efficient and powerful tools for studying critical and scaling phenomena in interacting many-particle systems. The multiloop Feynman diagrams underpin the specific…
We review the rigorous work on many Fermions models which lead to the first constructions of interacting Fermi liquids in two dimensions, and allowed to prove that there are different scaling regimes in two dimensions, depending on the…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
This paper explores the advanced mathematical frameworks used to analyze symmetry breaking in high-dimensional field theories, emphasizing the roles of Laurent series, residues, and winding numbers. Symmetry breaking is fundamental in…
We present a generalized framework, renormalized density matrix downfolding (RDMD), to derive systematically improvable, highly accurate, and nonperturbative effective models from ab initio calculations. This framework moves beyond the…
Nonlocal effective interactions are inherent to non-relativistic quantum many-body systems, but their systematic resummation poses a significant challenge known as the ``vertex problem" in many-body perturbation theory. We introduce a…
We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each…
We use scaling and renormalization-group techniques to analyze the leading nonanalyticities in a Fermi liquid. We show that a physically motivated scaling hypothesis reproduce the results known from perturbation theory for the density of…
In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently re-emerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this…
Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of theoretical Physics. The two problems…
Data augmentation methods are commonly integrated into the training of anomaly detection models. Previous approaches have primarily focused on replicating real-world anomalies or enhancing diversity, without considering that the standard of…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
We discuss renormalization group approaches to strongly interacting Fermi systems, in the context of Landau's theory of Fermi liquids and functional methods, and their application to neutron matter.
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
We review the field-theoretic renormalization-group approach to critical properties of flat polymerized membranes. We start with a presentation of the flexural effective model that is entirely expressed in terms of a transverse (flexural)…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac…