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Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States.

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Finite-size fermionic tensor networks, combined with variational Monte Carlo, accurately simulate the 2D Hubbard model. This approach surpasses existing methods, revealing physics like dimensional crossover in doped lattices.

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Area of Science:

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

Background:

  • The 2D Hubbard model is a fundamental model for understanding strongly correlated electron systems, crucial for explaining phenomena like high-temperature superconductivity.
  • Accurate simulation of the 2D Hubbard model is computationally challenging due to its complex many-body interactions and large system sizes.

Purpose of the Study:

  • To demonstrate the efficacy of finite-size fermionic projected entangled pair states (PEPS) with variational Monte Carlo (VMC) for simulating the 2D Hubbard model.
  • To establish a new computational benchmark by surpassing state-of-the-art Density Matrix Renormalization Group (DMRG) results.
  • To investigate the physics of doped 2D Hubbard lattices, specifically the dimensional crossover between stripe orientations.

Main Methods:

  • Utilizing finite-size fermionic tensor networks, specifically projected entangled pair states (PEPS).
  • Employing variational Monte Carlo (VMC) as the optimization and sampling technique.
  • Comparing results against state-of-the-art Density Matrix Renormalization Group (DMRG) calculations on eight-leg ladders.

Main Results:

  • Achieved energies surpassing state-of-the-art DMRG results for eight-leg ladders, using bond dimensions up to D=28.
  • Successfully applied the finite-size fermionic PEPS-VMC method to 10×16, 12×16, and 16×16 lattices.
  • Observed the dimensional crossover between stripe orientations in 1/8 hole-doped lattices.

Conclusions:

  • Finite-size fermionic tensor networks offer a powerful and accurate method for simulating the 2D Hubbard model.
  • This methodology provides a viable alternative to DMRG for larger and more complex lattice structures.
  • The study resolves key physics in doped Hubbard models, paving the way for further investigations into correlated electron systems.