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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.