Related papers: Tensor network approach to 2D Yang-Mills theories
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 reconsider the renormalizability of topological Yang-Mills field theories in (anti-)self-dual Landau gauges. By employing algebraic renormalization techniques we show that there is only one independent renormalization. Moreover, due to…
We study $\mathrm{SU}(3)$ Yang-Mills theory in $(2+1)$ dimensions based on networks of Wilson lines. With the help of the $q$ deformation, networks respect the (discretized) $\mathrm{SU}(3)$ gauge symmetry as a quantum group, i.e.,…
Formulating non-Abelian gauge theories as a tensor network is known to be challenging due to the internal degrees of freedom that result in the degeneracy in the singular value spectrum. In two dimensions, it is straightforward to 'trace…
This article provides a Wilsonian description of the perturbatively renormalizable Tensorial Group Field Theory introduced in arXiv:1303.6772 [hep-th] (Commun. Math. Phys. 330, 581-637). It is a rank-3 model based on the gauge group SU(2),…
We propose a method to represent the path integral over gauge fields as a tensor network. We introduce a trial action with variational parameters and generate gauge field configurations with the weight defined by the trial action. We…
We present our progress on a study of the $O(3)$ model in two-dimensions using the Tensor Renormalization Group method. We first construct the theory in terms of tensors, and show how to construct $n$-point correlation functions. We then…
We numerically simulate a non-Abelian lattice gauge theory in two spatial dimensions, with tensor networks (TN), up to intermediate sizes (>30 matter sites) well beyond exact diagonalization. We focus on the SU(2) Yang-Mills model in…
A manifestly gauge invariant exact renormalization group for pure SU(N) Yang-Mills theory is proposed, allowing gauge invariant calculations, without any gauge fixing or ghosts. The necessary gauge invariant regularisation which implements…
We perform a tensor renormalization group simulation of non-Abelian gauge theory in three dimensions using a formulation based on the `armillary sphere.' In this formulation, matrix indices are completely traced out, eliminating the…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories,…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
The non-linear nature of Yang-Mills theory presents a challenge for extracting exact classical solutions, which are useful for understanding non-perturbative vacuum structures. In this paper, an algebraic tensor ring decomposition framework…
We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge…
A new set of tetrads is introduced within the framework of SU(2) X U(1) Yang-Mills field theories in four dimensional Lorentz curved spacetimes. Each one of these tetrads diagonalizes separately and explicitly each term of the Yang-Mills…
We introduce two-dimensional tensor network representations of finite groups carrying a 4-cocycle index. We characterize the associated gapped (2+1)D phases that emerge when these anomalous symmetries act on tensor network ground states. We…
Quantum properties of topological Yang-Mills theory in (anti-)self-dual Landau gauge were recently investigated by the authors. We extend the analysis of renormalizability for two generalized classes of gauges; each of them depending on one…
We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level…
We present a strategy for a non-perturbative determination of the finite renormalization constants of the energy-momentum tensor in the SU(3) Yang-Mills theory. The computation is performed by imposing on the lattice suitable Ward Identites…