Critical Ising Model with Boundary Magnetic Field: RG Interface and Effective Hamiltonians

Abstract

Critical 2D Ising model with a boundary magnetic field is arguably the simplest QFT that interpolates between two non-trivial fixed points. We use the diagonalising Bogolyubov transformation for this model to investigate two quantities. Firstly we explicitly construct an RG interface operator that is a boundary condition changing operator linking the free boundary condition with the one with a boundary magnetic field. We investigate its properties and in particular show that in the limit of large magnetic field this operator becomes the dimension 1/16 primary field linking the free and fixed boundary conditions. Secondly we use Schrieffer-Wolff method to construct effective Hamiltonians both near the UV and IR fixed points.

38 pages; v.2 minor changes, to appear in JHEP

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Cited by in corpus (4)

• Fermionic CFTs and classifying algebras
• Properties of RG interfaces for 2D boundary flows
• On asymptotic behaviour in truncated conformal space approach
• Ising model in a boundary magnetic field with random discontinuities