Fermion masses through four-fermion condensates

Ayyar, Venkitesh; Chandrasekharan, Shailesh

doi:10.1007/jhep10(2016)058

Cited by 47 publications

(57 citation statements)

References 67 publications

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“…It can be applied to a certain class of fermionic models and it has been found to be very efficient in solving these models. Application of the Fermion Bag approach to our model has been described in detail in [10].…”

Section: Computational Approachmentioning

confidence: 99%

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Search for a continuum limit of the PMS phase

Ayyar¹

2017

Proceedings of 34th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)

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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

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Section: Computational Approachmentioning

confidence: 99%

“…In this work, we look for a similar continuum limit of the PMS phase using the same model in 4 Euclidean dimensions. A detailed account of this study can be found in [10].…”

Section: Introductionmentioning

confidence: 99%

Search for a continuum limit of the PMS phase

Ayyar¹

2017

Proceedings of 34th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)

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“…[12]. The conclusion of that work was that a narrow broken phase * smcatter@syr.edu reappears upon lifting the theory from three to four dimensions.…”

Section: Introductionmentioning

confidence: 99%

Novel phases in strongly coupled four-fermion theories

Catterall

Schaich

2017

Phys. Rev. D

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We study a lattice model comprising four massless reduced staggered fermions in four dimensions coupled through an SU (4)-invariant four-fermion interaction. We present both theoretical arguments and numerical evidence that no bilinear fermion condensates are present for any value of the four-fermi coupling, in contrast to earlier studies of Higgs-Yukawa models with different exact lattice symmetries. At strong coupling we observe the formation of a four-fermion condensate and a mass gap in spite of the absence of bilinear condensates. Unlike those previously studied systems we do not find a ferromagnetic phase separating this strong-coupling phase from the massless weak-coupling phase. Instead we observe long-range correlations in a narrow region of the coupling, still with vanishing bilinear condensates. While our numerical results come from relatively small lattice volumes that call for caution in drawing conclusions, if this novel phase structure is verified by future investigations employing larger volumes it may offer the possibility for new continuum limits for strongly interacting fermions in four dimensions.

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“…For each flavor the sum gives the Pfaffian of a k × k matrix W ([x; k]), whose matrix elements are given by the free staggered fermion propagator G f (x i , x j ) between the sites in [x; k] [20]. Thus, we obtain…”

Section: The Partition Functionmentioning

confidence: 99%

“…For example it was recently studied extensively in three and four dimensions [17][18][19][20][21] and contains a weak coupling massless fermion phase and a strong coupling massive fermion phase without any spontaneous symmetry breaking. In three dimensions one finds a second order phase transition that separates these two phases.…”

Section: Introductionmentioning

confidence: 99%

Generating a nonperturbative mass gap using Feynman diagrams in an asymptotically free theory

Ayyar

Chandrasekharan

2017

Phys. Rev. D

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Using the example of a two dimensional four-fermion lattice field theory we demonstrate that Feynman diagrams can generate a mass gap when massless fermions interact via a marginally relevant coupling. We introduce an infrared cutoff through the finite system size so that the perturbation series for the partition function and observables become convergent. We then use the Monte Carlo approach to sample sufficiently high orders of diagrams to expose the presence of a mass gap in the lattice model.

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Fermion masses through four-fermion condensates

Cited by 47 publications

References 67 publications

Search for a continuum limit of the PMS phase

Search for a continuum limit of the PMS phase

Novel phases in strongly coupled four-fermion theories

Generating a nonperturbative mass gap using Feynman diagrams in an asymptotically free theory

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