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Efficient Tensor Network Ansatz for High-Dimensional Quantum Many-Body Problems.

Timo Felser1,2,3, Simone Notarnicola2,3,4, Simone Montangero2,3,4

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We developed a new tensor network structure for quantum many-body wave functions. This scalable method achieves high precision for 2D spin models and Rydberg atom simulations, revealing new quantum phases.

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Area of Science:

  • Quantum Many-Body Physics
  • Computational Physics

Background:

  • Tree tensor networks are established for representing quantum wave functions.
  • Efficiently simulating large quantum systems remains a challenge.

Purpose of the Study:

  • Introduce a novel tensor network structure.
  • Enhance scalability and precision in quantum simulations.
  • Investigate 2D quantum systems, including Rydberg atoms.

Main Methods:

  • Augmenting tree tensor network representation with a new structure.
  • Benchmarking against 2D spin models.
  • Computing ground state phase diagrams for 2D lattice Rydberg atoms.

Main Results:

  • The new structure satisfies the area law in high dimensions.
  • Achieved unprecedented precision and system sizes for 2D spin models.
  • Observed nontrivial phases and quantum phase transitions in Rydberg atom systems.

Conclusions:

  • The novel tensor network structure is efficient, scalable, and precise.
  • Provides realistic benchmarks for current and future 2D quantum simulations.
  • Enables the study of complex quantum phenomena in Rydberg atom systems.