Tensor network methods for extracting conformal field theory data from fixed-point tensors and defect coarse graining

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Computational Physics

Background:

• Tensor network methods are powerful tools for studying quantum many-body systems.
• The tensor renormalization group (TRG) provides a framework for coarse-graining tensor networks.
• Understanding critical phenomena in the 2D Ising model is a fundamental problem.

Purpose of the Study:

• To extract conformal field theory data from tensor network representations.
• To investigate the impact of lattice defects on the coarse-graining process.
• To analyze the capabilities and limitations of TRG methods for defected systems.

Main Methods:

• Utilizing the fixed-point tensor of the linearized tensor renormalization group (lTRG).
• Introducing pointlike defects into the lattice to study their effects.
• Employing graph-independent local truncation (GILT) and higher-order tensor renormalization group (HOTRG) methods.
• Applying the minimal canonical form to enhance RG flow stability.

Main Results:

• Extracted operator scaling dimensions and operator product expansion coefficients.
• Established a correspondence between coarse-grained defect tensors and conformal states.
• Demonstrated that GILT+HOTRG can yield accurate two- and four-point functions under specific conditions.
• Showed improved RG flow stability with the minimal canonical form.

Conclusions:

• The study enhances understanding of tensor renormalization group (TRG) capabilities in coarse-graining defect tensors.
• The proposed methods offer accurate calculations for specific lattice defect configurations.
• The findings provide insights into applying tensor networks to systems with defects in critical phenomena.