Related papers: Renormalization group flow and fixed-point in tens…
In this study, the higher-order tensor renormalization group (HOTRG) method is applied to a lattice glass model that has local constraints on the occupation number of neighboring particles represented by many-body interactions. This model…
We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D…
We apply a recently developed numerical renormalization group, the corner-transfer-matrix renormalization group (CTMRG), to 2D classical lattice models at their critical temperatures. It is shown that the combination of CTMRG and the…
We develop the finite-size scaling (FSS) theory at quantum transitions, considering generic boundary conditions, such as open and periodic boundary conditions, and also the corrections to the leading FSS behaviors. Using…
We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group…
Recent findings indicate that over-parametrization, while crucial for successfully training deep neural networks, also introduces large amounts of redundancy. Tensor methods have the potential to efficiently parametrize over-complete…
We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard…
The renormalized zero-momentum four-point coupling $g_r$ of O(N)-invariant scalar field theories in $d$ dimensions is studied by applying the 1/N expansion and strong coupling analysis. The O(1/N) correction to the $\beta$-function and to…
We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
Recurrent Neural Network (RNN) are a popular choice for modeling temporal and sequential tasks and achieve many state-of-the-art performance on various complex problems. However, most of the state-of-the-art RNNs have millions of parameters…
We make Kadanoff's block idea into a reliable three-dimensional (3D) real space renormalization group (RG) method. Kadanoff's idea, expressed in spin representation, offers a qualitative intuition for clarifying scaling behavior in…
The linear transform-based tensor nuclear norm (TNN) methods have recently obtained promising results for tensor completion. The main idea of this type of methods is exploiting the low-rank structure of frontal slices of the targeted tensor…
The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…
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…
Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…
The renormalized zero-momentum four-point coupling $g_r$ of $O(N)$-invariant scalar field theories in $d$ dimensions is studied by applying the $1/N$ expansion and strong coupling analysis. The $O(1/N)$ correction to the $\beta$-function…
The tensor renormalization group is a promising numerical method used to study lattice statistical field theories. However, this approach is computationally expensive in 2+1 and 3+1 dimensions. Here we use tensor renormalization group…
The tensor renormalization group method is a promising approach to lattice field theories, which is free from the sign problem unlike standard Monte Carlo methods. One of the remaining issues is the application to gauge theories, which is…
We investigate finite lattice approximations to the Wilson Renormalization Group in models of unconstrained spins. We discuss first the properties of the Renormalization Group Transformation (RGT) that control the accuracy of this type of…