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Decoherence through Ancilla Anyon Reservoirs.

Nayan Myerson-Jain1, Taylor L Hughes2, Cenke Xu1

  • 1University of California, Santa Barbara, Department of Physics, California 93106, USA.

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This summary is machine-generated.

We study decoherence in topological orders using the 2D Toric code. Interactions with anyons reveal new correlations and localized Majorana zero modes on the boundary.

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Area of Science:

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

Background:

  • Topological orders exhibit exotic properties, including gapless boundaries.
  • Decoherence is a critical challenge in maintaining quantum states.
  • Anyons are quasiparticles with non-trivial braiding statistics.

Purpose of the Study:

  • To investigate the decoherence mechanisms of critical boundaries in topological orders.
  • To understand the role of ancilla anyons in boundary decoherence.
  • To analyze the impact of different anyon species on boundary properties.

Main Methods:

  • Utilizing the 2D Toric code as a model system.
  • Extending symmetry conditions to gauge invariance for decoherence.
  • Mapping boundary partition functions to 2D critical Ising models with defects.
  • Analyzing the relevance and marginality of anyon-induced line defects.

Main Results:

  • Relevant line defects for e and m anyons induce long-range correlations.
  • Marginal defect for f anyons leads to a line of fixed points with varying central charges.
  • Decoherence-analogs of Majorana zero modes appear at interfaces.
  • Universal logarithmic scaling of Rényi entropy observed.

Conclusions:

  • The nature of anyons dictates the decoherence dynamics and resulting boundary correlations.
  • Gauge invariance is crucial for describing decoherence in topological systems.
  • The study reveals novel phenomena like fixed-point lines and localized Majorana modes due to decoherence.