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.
Highlights
The motivation for this work comes from recent numerical studies [1,2,3,4,5,6,7,8] of a particular lattice four fermion theory constructed using reduced staggered fermions [9]
We explore the phase structure of a four dimensional SOð4Þ invariant lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a real scalar field
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 evidence of a diverging correlation length
Summary
The motivation for this work comes from recent numerical studies [1,2,3,4,5,6,7,8] of a particular lattice four fermion theory constructed using reduced staggered fermions [9]. In this paper we provide evidence in favor of this from direct numerical investigation of the lattice Higgs-Yukawa model This development presents the possibility of new critical behavior in a four-dimensional lattice theory of strongly interacting fermions, which would be very interesting from both theoretical and phenomenological viewpoints, and connects to recent activity within the condensed matter community [11,12]. We present numerical results for the phase structure of the theory in Sec. IV, and extend this investigation in Sec. V by adding symmetry-breaking source terms to the action in order to search for spontaneous symmetry breaking in the thermodynamic limit.
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