Tensor renormalization group approach to four-dimensional complex ${\varphi }^4$ theory at finite density

Abstract

Tensor network is an attractive approach to field theory with negative sign problem. The complex ${\varphi }^4$ theory at finite density is a test bed for numerical algorithms to verify their effectiveness. The model shows a characteristic feature called the Silver Blaze phenomenon associated with the sign problem in the large volume limit at low temperature. We analyze the four-dimensional model employing the anisotropic tensor renormalization group algorithm. We find a clear signal of the Silver Blaze phenomenon on a large volume of $V=1024^4$, which implies that the tensor network approach is effective even for four-dimensional field theory beyond two dimensions.

11 pages, 6 figures

References in corpus (25)

• Tensor renormalization group approach to 2D classical lattice models
• Coarse-graining renormalization by higher-order singular value decomposition
• Can stochastic quantization evade the sign problem? -- the relativistic Bose gas at finite chemical potential
• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem
• Grassmann Tensor Renormalization Group Approach to One-Flavor Lattice Schwinger Model
• 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
• Lattice study of the Silver Blaze phenomenon for a charged scalar phi-4 field
• Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger model with one flavor of Wilson fermion
• Complex Langevin dynamics at finite chemical potential: mean field analysis in the relativistic Bose gas
• 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
• Tensor network formulation of the massless Schwinger model
• Universal features of the Abelian Polyakov loop in 1+1 dimension
• Higher order tensor renormalization group for relativistic fermion systems
• Tensor network formulation for two-dimensional lattice $\mathcal{N}=1$ Wess-Zumino model
• Tensor renormalization group analysis of CP(N-1) model
• Application of neural network to sign problem via path optimization method
• Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group
• Tensor renormalization group study of two-dimensional U(1) lattice gauge theory with a $\theta$ term
• Investigation of complex ${\varphi }^4$ theory at finite density in two dimensions using TRG
• Phase transition of four-dimensional Ising model with tensor network scheme
• Canonical simulations with worldlines: an exploratory study in ${\varphi }_2^4$ lattice field theory

Cited by in corpus (24)

• Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Restoration of chiral symmetry in cold and dense Nambu--Jona-Lasinio model with tensor renormalization group
• Tensor renormalization group and the volume independence in 2D U($N$) and SU($N$) gauge theories
• Tensor renormalization group study of (3+1)-dimensional $Z_2$ gauge-Higgs model at finite density
• Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory
• Phase transition of four-dimensional lattice ${\varphi }^4$ theory with tensor renormalization group
• Critical endpoint of (3+1)-dimensional finite density $Z_3$ gauge-Higgs model with tensor renormalization group
• Tensor renormalization group approach to (1+1)-dimensional Hubbard model
• Loop-Free Tensor Networks for High-Energy Physics
• Triad second renormalization group
• Gauge invariant input to neural network for path optimization method
• Improving efficiency of the path optimization method for a gauge theory
• Tensor renormalization group approach to (1+1)-dimensional SU(2) principal chiral model at finite density
• Tensor renormalization group study of (1+1)-dimensional U(1) gauge-Higgs model at $\theta =\pi$ with Lüscher's admissibility condition
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Quantum Field Theories with Tensor Renormalization Group
• Grassmann tensor renormalization group approach to $(1+1)$-dimensional two-color lattice QCD at finite density
• Spectroscopy with the tensor renormalization group method
• Triad representation for the anisotropic tensor renormalization group in four dimensions
• Metal-insulator transition in (2+1)-dimensional Hubbard model with tensor renormalization group
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method
• Applying the Triad network representation to four-dimensional ATRG method
• Tensor renormalization group study of cold and dense QCD in the strong coupling limit