Renormalization of the vacuum angle for a particle on a ring

2006/07/04 by S. M. Apenko
Physics and Astronomy · #Charge (physics) #Density matrix renormalization group #Functional renormalization group #Magnetic field #Mathematical physics #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Renormalization #Renormalization group #Ring (chemistry) #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.74.193311

published as Phys. Rev. B 74, 193311 (2006) · 4 pages, 1 figure

arxiv created 2006/07/04 · openalex publication_date 2006/11/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We analyze the vacuum (topological) angle \ensuremathθ renormalization for the quantum mechanical model of a particle moving around a ring, where \ensuremathθ is the magnetic flux through the ring. We construct a renormalization group (RG) transformation for this model and derive exact RG equations which lead to the flow diagram similar to that of the quantum Hall effect. Renormalization of \ensuremathθ is seen to follow from the loss of information about the initial topological charge in the course of the RG procedure.

Citations

• Aharonov-Bohm oscillations of a particle coupled to dissipative environments
• The renormalization group: Critical phenomena and the Kondo problem
• General topological features and instanton vacuum in quantum Hall and spin liquids
• Quantum spin chains and the Haldane gap
• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State