Scaling Hypothesis for Projected Entangled-Pair States

Area of Science:

• Physics
• Computational Physics
• Condensed Matter Physics

Background:

• Strongly correlated systems present significant computational challenges for simulations.
• Projected entangled-pair states (PEPS) are a powerful tensor network method for these systems.
• Extrapolating PEPS data often requires large bond dimensions and extensive computational resources.

Purpose of the Study:

• To introduce a novel paradigm for scaling PEPS simulations.
• To enable reliable extrapolations of PEPS data for critical systems using smaller bond dimensions.
• To circumvent the need for extrapolations in the environment bond dimension (χ).

Main Methods:

• Utilizing the effective correlation length (ξ) to collapse PEPS data points, f(D,χ)=f(ξ(D,χ)).
• Optimizing PEPS using a fixed-χ gradient method.
• Employing a novel tensor-network algorithm for 2D transfer matrix fixed points or backwards differentiation.

Main Results:

• Demonstrated a method for reliable PEPS data extrapolation with smaller bond dimensions (D).
• Successfully circumvented the need for χ extrapolations, allowing more data points for fixed D.
• Validated the approach on critical 3D dimer and Ising models, and the 2D quantum Heisenberg model.

Conclusions:

• The proposed method offers a more efficient and reliable way to simulate critical strongly correlated systems.
• This paradigm shift in PEPS simulations simplifies data analysis and reduces computational cost.
• The technique is broadly applicable to various critical quantum and classical models.