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Extracting Higher Central Charge from a Single Wave Function.

Ryohei Kobayashi1, Taige Wang2,3, Tomohiro Soejima2

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Researchers developed a quantum computing method to identify obstructions in topologically ordered phases. This helps determine if a phase has a gappable edge, crucial for understanding quantum materials.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory
  • Topological Phases of Matter

Background:

  • Topologically ordered phases in (2+1) dimensions can possess gappable edges, but this is not always guaranteed, even with vanishing chiral central charge (c_{-}).
  • A recently identified 'higher' central charge acts as an additional obstruction to gapping the edge, beyond the conventional c_{-}.
  • Understanding edge properties is vital for classifying and utilizing topological phases in quantum technologies.

Purpose of the Study:

  • To characterize higher central charges using the expectation value of a partial rotation operator on a quantum state.
  • To establish a numerical method for extracting these higher central charges from a single wave function.
  • To provide a complete criterion for determining if a (2+1)D bosonic topological order has a gappable edge.

Main Methods:

  • Analytical derivation from modular properties of edge conformal field theories.
  • Numerical evaluation of the partial rotation operator's expectation value on specific wave functions.
  • Testing with the $\nu=1/2$ bosonic Laughlin state (U(1)$_2$ topological order) and the Kitaev honeycomb model's non-Abelian phase (Ising topological order).

Main Results:

  • Higher central charges are directly related to the expectation value of the partial rotation operator.
  • This expectation value can be computed from a single wave function, making it accessible via quantum computation.
  • A numerical method is established to identify obstructions to gappable edges in (2+1)D bosonic topological orders beyond c_{-}.
  • The method allows for complete determination of gappable edges in (2+1)D bosonic Abelian topological orders.

Conclusions:

  • The expectation value of the partial rotation operator provides a powerful tool for characterizing higher central charges and obstructions to gappable edges.
  • This work enables the complete classification of gappable edges in (2+1)D bosonic Abelian topological orders.
  • The findings impose constraints on the low-energy spectrum of bulk-boundary systems, analogous to Lieb-Schultz-Mattis theorems.