Fixed point annihilation for a spin in a fluctuating field

Abstract

A quantum spin impurity coupled to a critical free field (the Bose-Kondo model) can be represented as a 0+1D field theory with long-range-in-time interactions that decay as $|t-t^{\prime }{|}^{-(2-\delta )}$. This theory is a simpler analogue of nonlinear sigma models with topological Wess-Zumino-Witten terms in higher dimensions. In this note we show that the RG flows for the impurity problem exhibit an annihilation between two nontrivial RG fixed points at a critical value ${\delta }_c$ of the interaction exponent. The calculation is controlled at large spin $S$. This clarifies the phase diagram of the Bose-Kondo model and shows that it serves as a toy model for phenomena involving fixed-point annihilation and "quasiuniversality" in higher dimensions.

4 pages, 1 figure

References in corpus (11)

• "Deconfined" quantum critical points
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Quantum phase transitions in the Bose-Fermi Kondo model
• Quantum critical properties of the Bose-Fermi Kondo Model in a large-N limit
• Spin Impurities, Wilson Lines and Semiclassics
• Frustration of Decoherence in Open Quantum Systems
• Spectral function of a localized fermion coupled to the Wilson-Fisher conformal field theory
• Wilson loop in general representation and RG flow in 1d defect QFT
• The pseudogap Fermi-Bose Kondo model
• Quantum Monte Carlo simulation of spin-boson models using wormhole updates
• Quantum impurity in a magnetic environment

Cited by in corpus (11)

• Phases of Wilson Lines in Conformal Field Theories
• Wilson loop in general representation and RG flow in 1d defect QFT
• Reclaiming the Lost Conformality in a non-Hermitian Quantum 5-state Potts Model
• SU(2)-Symmetric Spin-Boson Model: Quantum Criticality, Fixed-Point Annihilation, and Duality
• Complex entanglement entropy for complex conformal field theory
• Critical phase induced by Berry phase and dissipation in a spin chain
• The Aubry-Andre Anderson model: Magnetic impurities coupled to a fractal spectrum
• Persistent Corner Spin Mode at the Quantum Critical Point of a Plaquette Heisenberg Model
• Continuous order-to-order quantum phase transitions from fixed-point annihilation
• Tunable phase transition in a dissipative two-spin system: A renormalization group study
• Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model