Search for a continuum limit of the PMS phase

Abstract

Previous studies of a simple four-fermion model with staggered fermions in 3D have shown the existence of an exotic quantum critical point, where one may be able to define a continuum limit of the Paramagnetic Strong Phase (or the PMS phase). We believe the existence of the critical point suggests a new mechanism for generating fermion masses. In this work we begin the search for this quantum critical point in 4D by extending the 3D model to 4D. Unlike in 3D, now we do find evidence for an intermediate spontaneously broken phase (FM phase) and are able compute the phase boundaries accurately. In terms of the bare coupling, the width of the intermediate region appears to be quite small. 34th annual International Symposium on Lattice Field Theory

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

“…In this paper we have reported on investigations of the phase diagram of a four-dimensional lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a scalar field transforming in the self-dual representation of a global SO(4) symmetry. This extends recent work on a related four fermion model in which a massless symmetric phase is separated from a massive symmetric phase by a narrow broken symmetry phase characterized by a small antiferromagnetic bilinear fermion condensate [5][6][7][8].…”

“…When this theory is lifted to four dimensions, however, a very narrow symmetry broken phase reappears characterized by a small bilinear condensate [5][6][7][8]. In Ref.…”

“…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 three dimensions this theory appears to exist in two phases -a free massless phase and a phase in which the fermions acquire a mass [1][2][3][4].…”

Phases of a strongly coupled four-fermion theory

“…The main change is a developing signal for spontaneous symmetry breaking in the critical region, potentially consistent with the results of Refs. [15,16]. We conclude in Section 4 with our plans to solidify this result and more carefully study the two transitions that a broken intermediate phase would imply.…”

“…Since the system we study possesses different exact lattice symmetries than those considered earlier, a priori it is possible that this two-phase structure may persist in four dimensions. The first Speaker, e-mail: schaich@itp.unibe.ch arXiv:1710.08137v1 [hep-lat] 23 Oct 2017 work exploring the four-dimensional theory reported the reappearance of a broken FM phase [15,16]. However, in contrast to the earlier studies this intermediate phase was very narrow, and the transitions bounding it appeared consistent with second-order criticality with mean-field exponents.…”