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Molecular Dynamics (MD) is a powerful computational microscope for probing protein functions. However, the need for fine-grained integration and the long timescales of biomolecular events make MD computationally expensive. To address this,…
The Renormalization Group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
Compared to ground state electronic structure optimizations, accurate simulations of molecular real-time electron dynamics are usually much more difficult to perform. To simulate electron dynamics, the time-dependent density matrix…
We summarize our recent efforts to develop the Density Matrix Renormalization Group (DMRG) method into a practical truncation strategy for large-scale nuclear shell model calculations. Following an overview of the essential features of the…
At low energies, the microscopic characteristics and changes of physical systems as viewed at different distance scales are described by universal scale invariant properties investigated by the Renormalization Group (RG) apparatus, an…
Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and…
Computational modeling of assembly is challenging for many systems because their timescales vastly exceed those accessible to simulations. This article describes the MultiMSM, which is a general framework that uses Markov state models…
Density Matrix Renormalization Group (DMRG) or Matrix Product States (MPS) are widely acknowledged as highly effective and accurate methods for solving one-dimensional quantum many-body systems. However, the direct application of DMRG to…
Large strongly correlated systems provide a challenge to modern electronic structure methods, because standard density functionals usually fail and traditional quantum chemical approaches are too demanding. The density-matrix…
We develop a novel real-space renormalization group (RG) scheme which accurately estimates correlation length exponent $\nu$ near criticality of higher-dimensional quantum Ising and Potts models in a transverse field. Our method is…
The Similarity Renormalization Group (SRG) is investigated as a powerful yet practical method to modify nuclear potentials so as to reduce computational requirements for calculations of observables. The key feature of SRG transformations…
The density matrix renormalization group (DMRG) is a celebrated tensor network algorithm, which computes the ground states of one-dimensional quantum many-body systems very efficiently. Here we propose an improved formulation of continuous…
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 compute the low energy threshold corrections to neutrino masses and mixing in the Standard Model (SM) and its minimal supersymmetric version, using the effective theory technique. We demonstrate that they stabilize the renormalization…
We analyze perturbative dynamics of a composite system consisting of a quantum mechanical system and an environment by the renormalization group (RG) method. The solution obtained from the RG method has no secular terms and approximates the…
Exploring and understanding topological phases in systems with strong distributed disorder requires developing fundamentally new approaches to replace traditional tools such as topological band theory. Here, we present a general real-space…
Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between…
The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…
The renormalization group (RG) method is extended for global asymptotic analysis of discrete systems. We show that the RG equation in the discretized form leads to difference equations corresponding to the Stuart-Landau or Ginzburg-Landau…