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Conformal properties of hyperinvariant tensor networks.

Matthew Steinberg1,2, Javier Prior3,4

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Hyperinvariant tensor networks (hyMERA) offer a promising approach for simulating hyperbolic conformal field theories. This study analyzes tensor optimization challenges and introduces new decompositions, finding compatibility with minimal model CFTs.

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Area of Science:

  • Theoretical Physics
  • Quantum Information
  • Condensed Matter Physics

Background:

  • Hyperinvariant tensor networks (hyMERA) combine perfect tensor networks (HaPPY) and multiscale entanglement renormalization ansatz (MERA) for AdS/CFT correspondence simulations.
  • hyMERA shows potential for simulating conformal field theories on hyperbolic manifolds with quasiperiodic boundaries, but faces unresolved challenges.

Purpose of the Study:

  • Analyze tensor optimization challenges in hyMERA for quasiperiodic critical spin chains.
  • Compare hyMERA optimization with standard MERA approaches.
  • Investigate new tensor decompositions and their implications for hyMERA construction.
  • Assess the compatibility of hyMERA spectral constraints with minimal model CFTs.

Main Methods:

  • Tensor network optimization techniques applied to hyMERA.
  • Comparative analysis of hyMERA and MERA optimization strategies.
  • Development and analysis of novel tensor decompositions.
  • Randomized trials using descending superoperators and spectral analysis.

Main Results:

  • Identified challenges in optimizing hyMERA tensors for quasiperiodic critical spin chains.
  • Introduced two new tensor decompositions with distinct properties, suggesting non-uniqueness and potential for generalization.
  • Demonstrated that spectral constraints in hyMERA are compatible with minimal model CFT operator spectra.

Conclusions:

  • hyMERA offers a viable framework for simulating specific quantum systems, despite optimization complexities.
  • The non-uniqueness of tensor decompositions suggests flexibility and potential for new analytical forms in hyMERA.
  • The spectral compatibility supports hyMERA's applicability to realistic conformal field theories.