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The similarity renormalization group (SRG) is based on unitary transformations that suppress off-diagonal matrix elements, forcing the hamiltonian towards a band-diagonal form. A simple SRG transformation applied to nucleon-nucleon…
Inspired by the superblock method of White, we introduce a simple modification of the standard Renormalization Group (RG) technique for the study of quantum lattice systems. Our method which takes into account the effect of Boundary…
We study the critical properties of the weakly disordered two-dimensional Ising and Baxter models in terms of the renormalization group (RG) theory generalized to take into account the replica symmetry breaking (RSB) effects. Recently it…
We propose and study a renormalization group transformation that can be used also for models with strong quenched disorder, like spin glasses. The method is based on a mapping between disorder distributions, chosen such as to keep some…
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the…
The three-dimensional Abelian Chern-Simons theory coupled to a scalar and a fermionic field of arbitrary charge is considered in order to study conformal symmetry breakdown and the effective potential stability. We present an improved…
We present a detailed description of the recently proposed numerical renormalization group method for models of quantum impurities coupled to a bosonic bath. Specifically, the method is applied to the spin-boson model, both in the Ohmic and…
We study the critical properties of the weakly disordered $p$-component ferromagnet in terms of the renormalization group (RG) theory generalized to take into account the replica symmetry breaking (RSB) effects coming from the multiple…
The density matrix renormalization group is applied to a relativistic complex scalar field at finite chemical potential. The two-point function and various bulk quantities are studied. It is seen that bulk quantities do not change with the…
The inverse renormalization group is studied based on the image super-resolution using the deep convolutional neural networks. We consider the improved correlation configuration instead of spin configuration for the spin models, such as the…
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…
A simple backreaction problem in quantum mechanics, the full quantum anharmonic oscillator, and quantum parametric resonance are studied using Renormalization Group techniques for global asymptotic analysis. In this short note this…
A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock,…
A simple phenomenological real-space renormalization group method for quantum Heisenberg spins with nearest and next nearest neighbour interactions on a pyrochlore lattice is presented. Assuming a scaling law for the order parameter of two…
A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration,…
Functional renormalization group (FRG) has become a diverse and powerful tool to derive effective low-energy scattering vertices of interacting many-body systems. Starting from a non-interacting expansion point of the action, the flow of…
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining…
We introduce a concise quantum operator formula for bosonization in which the Lie group structure appears in a natural way. The connection between fermions and bosons is found to be exactly the connection between Lie group elements and the…
We report on recent progress of the implementation of the similarity renormalization group (SRG) for three-body interactions in a one-dimensional, bosonic model system using the plane wave basis. We discuss our implementation of the flow…
The locality of field theories strongly constrains the possible behaviors of symmetry-twisted partition functions, and thus they serve as order parameters to detect low-energy realizations of global symmetries, such as spontaneous symmetry…