The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory

10 Aug 2022, 15:00

20m

CP1-HSZ/1.004 (CP1-HSZ) - HS7 (CP1-HSZ)

Oral Presentation Algorithms (including Machine Learning, Quantum Computing, Tensor Networks) Algorithms

Speaker

Takaaki Kuwahara (Shizuoka University)

Description

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 construct initial tensors with indices labelling these gauge field configurations. We perform the tensor renormalization group with the initial tensors and optimize the variational parameters. As a first step to the TRG study of non-Abelian gauge theory in more than two dimensions, we apply this method to three-dimensional pure SU(2) gauge theory. Our result for the free energy agrees with the analytical results in weak and strong coupling regimes.

Presentation materials

lattice2022_3dSU2.pdf