Boundary critical behavior of the Gross-Neveu-Yukawa model

Abstract

We study the critical behavior of the semi-infinite Gross-Neveu-Yukawa model, a quantum field theory describing Dirac fermions interacting with bosonic fields via a Yukawa coupling. We consider Neumann and Dirichlet boundary conditions for the bosonic fields, and the most general boundary conditions for the fermions that preserve unitarity, conformal invariance, and charge conjugation symmetry. We analyze the phase diagram and identify distinct fixed points corresponding to different universality classes of boundary critical behavior. The associated boundary critical exponents, which govern the scaling behavior and crossover phenomena, are computed to one-loop order. We also discuss the relevance of our results to the semi-infinite pseudoscalar Yukawa model.

Figures (2)

• Figure 1: RG flow and fixed points in the $(\phi,c)$ plane. Although the matrix $M$ given by Eq. \ref{['eq:M-phi']} itself is $2\pi$-periodic in $\phi$, the RG flows exhibit an effective periodicity of $\pi$. There are 6 independent FPs: corresponding to ordinary ($c^*=\infty$), special($c=c^*_{\rm sp}$), extraordinary ($c^*=-\infty$) transitions with TRI ($\phi^*=\pm\frac{\pi}{2}$) and without TRI ($\phi^*=0$). The TRI FPs are unstable with respect to non-TRI perturbations.
• Figure 2: The phase diagram exhibits three distinct phases: (i) both bulk and boundary ordered, (ii) bulk disordered but boundary ordered, and (iii) both bulk and boundary disordered. These phases are separated by the ordinary, extraordinary, and surface transition lines, which meet at the line of special transitions. Each of these transitions belongs to a non-TRI universality class for $|\phi| < \frac{\pi}{2}$, and to a TRI universality class for $\phi = \pm \frac{\pi}{2}$. The corresponding critical exponents for the TRI and non-TRI ordinary and special universality classes are summarized in Tab. \ref{['tab:1-dimensions']}