Related papers: Efficient implementation of the Time Renormalizati…
In this article we wish to present a new method to obtain spectral functions at finite temperature and density from the Functional Renormalization Group (FRG). The FRG offers a powerful non-perturbative tool to deal with phase transitions…
Perturbation theory is a crucial tool for many physical systems, when exact solutions are not available, or nonperturbative numerical solutions are intractable. Naive perturbation theory often fails on long timescales, leading to secularly…
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for…
Numerical approaches are an important tool to study strongly correlated quantum systems. However, their fragility with respect to rounding errors is not well studied and numerically verified enclosures of the results are not available. In…
We propose a new tensor renormalization group algorithm, Anisotropic Tensor Renormalization Group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the Higher-Order Tensor…
We apply the projective truncation technique to the tensor renormalization group (TRG) algorithm in order to reduce the computational cost from $O(\chi^6)$ to $O(\chi^5)$, where $\chi$ is the bond dimension, and propose three kinds of…
Numerical studies are reported to support the idea to explain the particle production in late inflationary era based on the parametric resonance with a noise effect. Two nonperturbative renormalization group formulations are used to…
I compute a renormalization group (RG) improvement to the standard beyond-linear-order Eulerian perturbation theory (PT) calculation of the power spectrum of large-scale density fluctuations in the Universe. At z=0, for a power spectrum…
The authors propose a fast numerical renormalization group method --- the product wave function renormalization group (PWFRG) method --- for 1D quantum lattice models and 2D classical ones. A variational wave function, which is expressed by…
In this paper, we perform a comprehensive study of the renormalization group (RG) method on thermal tensor networks (TTN). By Trotter-Suzuki decomposition, one obtains the 1+1D TTN representing the partition function of 1D quantum lattice…
Describing the emergence of phases of condensed matter is one of the central challenges in physics. For this purpose many numerical and analytical methods have been developed, each with their own strengths and limitations. The functional…
We propose a second renormalization group (SRG) in the triad representation of tensor networks. The SRG method improves two parts of the triad tensor renormalization group, which are the decomposition of intermediate tensors and the…
We reformulate the density matrix renormalization group method (DMRG) in terms of a single block, instead of the standard left and right blocks used in the construction of the superblock. This version of the DMRG, which we call the puncture…
In this paper, we introduce a modified version of the renormalization group (RG) method and test its numerical accuracy. It has been tested on numerous scalar ODEs and systems of ODEs. Our method is primarily motivated by the possibility of…
We implement and apply time-dependent density matrix renormalization group (TD-DMRG) algorithms at zero and finite temperature to compute the linear absorption and fluorescence spectra of molecular aggregates. Our implementation is within a…
A semi-analytic approach to the computation of the non-linear power-spectrum of dark matter density fluctuations is proposed. The method is based on the Renormalization Group technique and can be applied to any underlying cosmological…
We present a numerical implementation of the renormalization group (RG) for partial differential equations, constructing similarity solutions and travelling waves. We show that for a large class of well-localized initial conditions,…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
Expanding and improving the repertoire of numerical methods for studying quantum lattice models is an ongoing focus in many-body physics. While the density matrix renormalization group (DMRG) has been established as a practically useful…
In this paper recent substantial progress in applying the density-matrix renormalization-group (DMRG) to the simulation of the time-evolution of strongly correlated quantum systems in one dimension is reviewed. Various approaches to…