Decoherence through Ancilla Anyon Reservoirs.

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.