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Projected entangled-pair states efficiently represent critical fermionic systems with 1D and 0D Fermi surfaces. Increasing the bond dimension controllably improves energy precision, enabling arbitrary accuracy for these quantum systems.

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Area of Science:

  • Quantum Many-Body Physics
  • Condensed Matter Theory
  • Computational Physics

Background:

  • Critical fermionic systems present significant challenges in theoretical physics.
  • Representing ground states of such systems requires advanced computational methods.
  • Understanding Fermi surfaces in 1D and 0D is crucial for condensed matter phenomena.

Purpose of the Study:

  • To demonstrate the efficacy of projected entangled-pair states (PEPS) for critical fermionic systems.
  • To investigate the scaling properties of PEPS in representing ground states.
  • To explore the potential for achieving arbitrary energy precision.

Main Methods:

  • Utilizing fermionic projected entangled-pair states (fPEPS) on a 2D lattice.
  • Applying a Gaussian restriction to the fPEPS.
  • Extrapolating finite-size results to the thermodynamic limit.
  • Analyzing energy precision as a function of bond dimension.

Main Results:

  • PEPS efficiently represent ground states of critical fermionic systems with 1D and 0D Fermi surfaces.
  • Energy precision improves as a power law with increasing bond dimension.
  • Arbitrary precision can be achieved by controlled increases in bond dimension.

Conclusions:

  • fPEPS provide an efficient and accurate method for studying critical fermionic systems.
  • The bond dimension scaling offers a pathway to high-precision calculations.
  • Careful selection of boundary conditions and system sizes is necessary to avoid Ansatz nonanalyticities.