Reduced tensor network formulation for non-Abelian gauge theories in arbitrary dimensions

Abstract

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 out' these degrees of freedom with the use of character expansion, giving a reduced tensor network where the degeneracy associated with the internal symmetry is eliminated. In this work, we show that such an index loop also exists in higher dimensions in the form of a closed tensor network we call the 'armillary sphere'. This allows us to completely eliminate the matrix indices and reduce the overall size of the tensors in the same way as is possible in two dimensions. This formulation allows us to include significantly more representations with the same tensor size, thus making it possible to reach a greater level of numerical accuracy in the tensor renormalization group computations.

arXiv comment15 pages, 9 figures; v2: reference added; v3: reference added & eq(3.4) corrected

References in corpus (19)

• Tensor renormalization group approach to 2D classical lattice models
• Coarse-graining renormalization by higher-order singular value decomposition
• Tensor Network Renormalization
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Exact blocking formulas for spin and gauge models
• A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Anisotropic Tensor Renormalization Group
• Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion
• Tensor renormalization group study of the non-Abelian Higgs model in two dimensions
• Efficient simulation of Grassmann Tensor Product States
• Higher order tensor renormalization group for relativistic fermion systems
• The dual of pure non-Abelian lattice gauge theory as a spin foam model
• Tensor renormalization group study of two-dimensional U(1) lattice gauge theory with a $\theta$ term
• Tensor renormalization group and the volume independence in 2D U($N$) and SU($N$) gauge theories
• Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory
• Grassmann higher-order tensor renormalization group approach for two-dimensional strong-coupling QCD
• Critical endpoint of (3+1)-dimensional finite density $Z_3$ gauge-Higgs model with tensor renormalization group
• GrassmannTN: a Python package for Grassmann tensor network computations

Cited by in corpus (1)

• Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $\theta =\pi$ from imaginary $\theta$ simulations