Related papers: Comparing Tensor Renormalization Group and Monte C…
Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group (TRG) formulation allows one to write exact, compact, and manifestly local…
The idea of blocking in configuration space has played an important role in the development of the RG ideas. However, despite being half a century old and having had a huge intellectual impact, generic numerical methods to perform blocking…
We study the $SU(2)$ gauge-Higgs model in two Euclidean dimensions using the tensor renormalization group (TRG) approach. We derive a tensor formulation for this model in the unitary gauge and compare the expectation values of different…
We consider the sign problem for classical spin models at complex $\beta =1/g_0^2$ on $L\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\beta$ than the reweighting Monte…
Tensor renormalization group method (TRG) is a real space renormalization group approach. It has been successfully applied to both classical and quantum systems. In this paper, we study a disordered and frustrated system, the…
We report recent progress on the application of the tensor renormalization group (TRG) to quantum field theories pursued by the Tsukuba group. We explain how to treat the scalar, fermion, and gauge theories with the TRG method presenting…
We discuss the reformulation of the O(2) model with a chemical potential and the Abelian Higgs model on a 1+1 dimensional space-time lattice using the Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and connects…
We describe a simple real space renormalization group technique for two dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum…
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 propose a modified form of a tensor renormalization group algorithm for evaluating partition functions of classical statistical mechanical models on 2D lattices. This algorithm coarse-grains only the rows and columns of the lattice…
We study the iteration of block spin transformations in the O(3) symmetric non-linear sigma-model on a two-dimensional square lattice with help of the Monte Carlo method. In contrast to the classical Monte Carlo Renormalization Group…
Tensor renormalization group (TRG) constitutes an important methodology for accurate simulations of strongly correlated lattice models. Facilitated by the automatic differentiation technique widely used in deep learning, we propose a…
We discuss the Tensor Renormalization Group (TRG) method for the O(2) model with a chemical potential in 1+1 dimensions with emphasis on near gapless/conformal situations. We emphasize the role played by the late Leo Kadanoff in the…
The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the…
We propose a new Real Space Renormalization Group transformation useful for Monte Carlo calculations in theories with global or local symmetries. From relaxation arguments we define the block-spin transformation with two tunable free…
The Time Renormalization Group (TRG) is an effective method for accurate calculations of the matter power spectrum at the scale of the first baryonic acoustic oscillations. By using a particular variable transformation in the TRG formalism,…
A linearized tensor renormalization group (LTRG) algorithm is proposed to calculate the thermodynamic properties of one-dimensional quantum lattice models, that is incorporated with the infinite time-evolving block decimation technique, and…
We propose a hybrid stochastic method for the tensor renormalization group (TRG) approach. TRG is known as a powerful tool to study the many-body systems and quantum field theory on the lattice. It is based on a low-rank approximation of…
We study constraint effective potentials for various strongly interacting $\phi^4$ theories. Renormalization group (RG) equations for these quantities are discussed and a heuristic development of a commonly used RG approximation is…
We analyze classical dimer models on the square and triangular lattice using a tensor network representation of the dimers. The correlation functions are numerically calculated using the recently developed "Tensor renormalization group"…