Tensor renormalization group and the volume independence in 2D U($N$) and SU($N$) gauge theories

Abstract

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 so far limited to U(1) and SU(2) gauge groups. In the case of higher rank, it becomes highly nontrivial to restrict the number of representations in the character expansion to be used in constructing the fundamental tensor. We propose a practical strategy to accomplish this and demonstrate it in 2D U($N$) and SU($N$) gauge theories, which are exactly solvable. Using this strategy, we obtain the singular-value spectrum of the fundamental tensor, which turns out to have a definite profile in the large-$N$ limit. For the U($N$) case, in particular, we show that the large-$N$ behavior of the singular-value spectrum changes qualitatively at the critical coupling of the Gross-Witten-Wadia phase transition. As an interesting consequence, we find a new type of volume independence in the large-$N$ limit of the 2D U($N$) gauge theory with the $\theta$ term in the strong coupling phase, which goes beyond the Eguchi-Kawai reduction.

arXiv comment40 pages, 19 figures

References in corpus (32)

• Tensor renormalization group approach to 2D classical lattice models
• Coarse-graining renormalization by higher-order singular value decomposition
• Tensor Network Renormalization
• Gauge-invariant implementation of the Abelian Higgs model on optical lattices
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• Large N reduction in the continuum three dimensional Yang-Mills theory
• Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N ?
• Tensor renormalization group study of classical XY model on the square lattice
• Critical behavior of lattice Schwinger model with topological term at $\theta =\pi$ using Grassmann tensor renormalization group
• Anisotropic Tensor Renormalization Group
• Grassmann tensor renormalization group for one-flavor lattice Gross-Neveu model with finite chemical potential
• 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
• Tensor network analysis of critical coupling in two dimensional ${\varphi }^4$ theory
• Phase transition of four-dimensional Ising model with higher-order tensor renormalization group
• Universal features of the Abelian Polyakov loop in 1+1 dimension
• Tensor network formulation of the massless Schwinger model
• Higher order tensor renormalization group for relativistic fermion systems
• Tensor network formulation for two-dimensional lattice $\mathcal{N}=1$ Wess-Zumino model
• Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group
• Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice
• Tensor renormalization group approach to four-dimensional complex ${\varphi }^4$ theory at finite density
• Tensor renormalization group study of two-dimensional U(1) lattice gauge theory with a $\theta$ term
• More about the Grassmann tensor renormalization group
• Restoration of chiral symmetry in cold and dense Nambu--Jona-Lasinio model with tensor renormalization group
• Phase transition of four-dimensional lattice ${\varphi }^4$ theory with tensor renormalization group
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• Tensor renormalization group approach to (1+1)-dimensional Hubbard model
• Simulating Yang-Mills theories with a complex coupling
• Density of states approach for lattice gauge theory with a $\theta$-term
• Topological effects in continuum 2d $U(N)$ gauge theories
• Tensor network approach to 2D Yang-Mills theories

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• Grassmann tensor renormalization group approach to $(1+1)$-dimensional two-color lattice QCD at finite density
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