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Researchers numerically demonstrated the annihilation of two renormalization-group (RG) fixed points in the spin-boson model. This finding reveals a stable strong-coupling phase and impacts critical magnet impurity moments.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Statistical Mechanics

Background:

  • The annihilation of renormalization-group (RG) fixed points is crucial in diverse physics fields.
  • Previous studies relied solely on perturbative techniques, limiting understanding.
  • The SU(2)-symmetric S=1/2 spin-boson model is a key system for studying quantum phase transitions.

Purpose of the Study:

  • To investigate the SU(2)-symmetric S=1/2 spin-boson model using high-accuracy quantum Monte Carlo methods.
  • To provide numerical evidence for the collision and annihilation of RG fixed points.
  • To explore the existence of a stable strong-coupling phase beyond perturbative RG predictions.

Main Methods:

  • High-accuracy quantum Monte Carlo simulations.
  • Detailed scaling analysis of the power-law bath spectrum (∝ω^{s}).
  • Exploitation of a duality and reflection symmetry in the RG beta function.

Main Results:

  • Direct numerical evidence for the collision and annihilation of two RG fixed points at s*=0.6540(2).
  • Discovery of a stable strong-coupling phase coexisting with a critical phase.
  • The critical phase disappears for spectral exponents s < s*.
  • Analytical predictions at strong coupling, derived from duality, show excellent agreement with numerical data.

Conclusions:

  • Fixed-point annihilation phenomena are now accessible to large-scale simulations.
  • The study reveals a surprising duality between RG fixed points, offering new analytical insights.
  • Implications for understanding impurity moments in critical magnets are discussed.