Related papers: Tensor renormalization group study of 3D principal…
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"…
Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…
We propose an improved tensor renormalization group (TRG) algorithm, the bond-weighted TRG (BTRG). In BTRG, we generalize the conventional TRG by introducing bond weights on the edges of the tensor network. We show that BTRG outperforms the…
We study the integrable bi-Yang-Baxter deformation of the $SU(2)$ principal chiral model (PCM) and its finite action uniton solutions. Under an adiabatic compactification on an $S^1$, we obtain a quantum mechanics with an elliptic…
We apply tensor network methods to study the strong-coupling $U(N)$ model in its dimer formulation. In three and four dimensions, we investigate the chiral condensate as a function of the quark mass and the degree of the symmetry group, and…
For the class of $1+1$ dimensional field theories referred to as the non-linear sigma models, there is known to be a deep connection between classical integrability and one-loop renormalizability. In this work, the phenomenon is reviewed on…
We study possible restoration patterns of chiral symmetry in a generalized hidden local symmetry model, which is a low energy effective theory of QCD including pseudo-scalar, vector and axial-vector mesons. We derive Wilsonian…
We introduce a numerical method to study critical properties near classical and quantum phase transitions. Our method applies ideas of the Tensor Renormalization Group to obtain an improved action which is used to extract critical…
We propose a new renormalization scheme of tensor networks made only of third order tensors. The isometry used for coarse-graining the network can be prepared at an $O(D^6)$ computational cost in any $d$ dimension ($d \ge 2$), where $D$ is…
We propose a method to compute the entanglement entropy (EE) using the tensor renormalization group (TRG) method. The reduced density matrix of a $d$-dimensional quantum system is represented as a $(d+1)$-dimensional tensor network. We…
The behavior of dimensionless quantities defined as ratios of partition functions is analyzed to investigate phase transitions and critical phenomena. At criticality, the universal values of these ratios can be predicted from conformal…
We identify new families of renormalizable of tensor models from anterior renormalizable tensor models via a mapping capable of reducing or increasing the rank of the theory without having an effect on the renormalizability property.…
We carry out a high-precision simulation of the two-dimensional $SU(3)$ principal chiral model at correlation lengths $\xi$ up to $\sim 4 \times 10^5$, using a multi-grid Monte Carlo (MGMC) algorithm and approximately one year of Cray C-90…
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…
Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor…
Anisotropic Tensor Renormalization Group (ATRG) is a powerful algorithm for four-dimensional tensor network calculations. However, the larger bond dimensions are known to be difficult to achieve in practice due to the higher computational…
We discuss the variational optimization of a unitary tensor-network circuit with different network structures. The ansatz is performed based on a generalization of well-developed multi-scale entanglement renormalization algorithm and also…
This thesis focuses on renormalization of quantum field theories. Its first part considers three tensor models in three dimensions, a Fermionic quartic with tensors of rank-3 and two Bosonic sextic, of ranks 3 and 5. We rely upon the…
Tensor models provide a way to access the path-integral for discretized quantum gravity in d dimensions. As in the case of matrix models for two-dimensional quantum gravity, the continuum limit can be related to a Renormalization Group…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…