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$SO(4)$ invariant Higgs-Yukawa model with reduced staggered fermions

Nouman Butt, Simon Catterall, David Schaich

TL;DR

This work extends a 4D SO(4) invariant lattice Higgs-Yukawa framework by adding a scalar kinetic term to a system of four reduced staggered fermions coupled to a self-dual scalar, enabling a search for a single continuous PMW–PMS transition without conventional order parameters. Through analytical limits and extensive lattice simulations, the authors identify a region where massless and massive symmetric phases remain separated by a direct, likely continuous transition in the absence of a fermion bilinear condensate, and they map preliminary bounds: $0 < κ_1 < 0.05$ and $0.085 < κ_2 < 0.125$. Negative κ regions exhibit antiferromagnetic bilinear condensation, while larger positive κ values induce a ferromagnetic phase, indicating a rich, non-Landau-like phase structure potentially governed by topological defects. The findings suggest the possibility of new fixed points in four-dimensional strongly interacting fermion systems and motivate further studies to tighten transition bounds and diagnose critical behavior via additional observables and scaling analyses.

Abstract

We explore the phase structure of a four dimensional $SO(4)$ invariant lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a real scalar field. The fermions belong to the fundamental representation of the symmetry group while the three scalar field components transform in the self-dual representation of $SO(4)$. The model is a generalization of a four fermion system with the same symmetries that has received recent attention because of its unusual phase structure comprising massless and massive symmetric phases separated by a very narrow phase in which a small bilinear condensate breaking $SO(4)$ symmetry is present. The generalization described in this paper simply consists of the addition of a scalar kinetic term. We find a region of the enlarged phase diagram which shows no sign of a fermion condensate or symmetry breaking but in which there is nevertheless evidence of a diverging correlation length. Our results in this region are consistent with the presence of a single continuous phase transition separating the massless and massive symmetric phases observed in the earlier work.

$SO(4)$ invariant Higgs-Yukawa model with reduced staggered fermions

TL;DR

This work extends a 4D SO(4) invariant lattice Higgs-Yukawa framework by adding a scalar kinetic term to a system of four reduced staggered fermions coupled to a self-dual scalar, enabling a search for a single continuous PMW–PMS transition without conventional order parameters. Through analytical limits and extensive lattice simulations, the authors identify a region where massless and massive symmetric phases remain separated by a direct, likely continuous transition in the absence of a fermion bilinear condensate, and they map preliminary bounds: and . Negative κ regions exhibit antiferromagnetic bilinear condensation, while larger positive κ values induce a ferromagnetic phase, indicating a rich, non-Landau-like phase structure potentially governed by topological defects. The findings suggest the possibility of new fixed points in four-dimensional strongly interacting fermion systems and motivate further studies to tighten transition bounds and diagnose critical behavior via additional observables and scaling analyses.

Abstract

We explore the phase structure of a four dimensional invariant lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a real scalar field. The fermions belong to the fundamental representation of the symmetry group while the three scalar field components transform in the self-dual representation of . The model is a generalization of a four fermion system with the same symmetries that has received recent attention because of its unusual phase structure comprising massless and massive symmetric phases separated by a very narrow phase in which a small bilinear condensate breaking symmetry is present. The generalization described in this paper simply consists of the addition of a scalar kinetic term. We find a region of the enlarged phase diagram which shows no sign of a fermion condensate or symmetry breaking but in which there is nevertheless evidence of a diverging correlation length. Our results in this region are consistent with the presence of a single continuous phase transition separating the massless and massive symmetric phases observed in the earlier work.

Paper Structure

This paper contains 7 sections, 19 equations, 16 figures.

Table of Contents

  1. Introduction
  2. Action and Symmetries
  3. Analytical results
  4. Phase Structure
  5. Fermion Bilinears
  6. Resulting phase diagram
  7. Summary and Conclusions

Figures (16)

  • Figure 1: $\left\langle \sigma^2_{+} \right\rangle$ vs $G$ for $L = 8$, comparing $\kappa = \pm0.05$ and 0.
  • Figure 2: $\chi_{\text{stag}}$ vs $G$ at $\kappa=0$ for $L=4$, 8 and 12.
  • Figure 3: $\chi_{\text{stag}}$ vs $G$ at $\kappa=-0.05$ for $L=6$, 8 and 12.
  • Figure 4: $\chi_{\text{stag}}$ vs $G$ at $\kappa=0.05$ for $L=6$, 8 and 12.
  • Figure 5: The ferromagnetic susceptibility $\chi_{\text{f}}$ vs $G$ at $\kappa=0.05$ for $L=6$, 8 and 12. Unlike the other susceptibility plots, the y-axis scale is not logarithmic.
  • ...and 11 more figures