Dynamical mass generation in pseudoquantum electrodynamics with four-fermion interactions

Dynamical mass generation in pseudoquantum electrodynamics with four-fermion interactions We describe dynamical symmetry breaking in a system of massless Dirac fermions with both electromagnetic and four-fermion interactions in (2+1) dimensions. The former is described by the pseudo quantum electrodynamics, and the latter is given by the so-called Gross-Neveu action. We apply the Hubbard-Stratonovich transformation and the large-Nf expansion in our model to obtain a Yukawa action. Thereafter, the presence of a symmetry broken phase is inferred from the nonperturbative Schwinger-Dyson equation for the electron propagator. This is the physical solution whenever the fine-structure constant is larger than a critical value αc(DNf). In particular, we obtain the critical coupling constant αc≈0.36 for DNf=8., where D=2, 4 corresponds to the SU(2) and SU(4) cases, respectively, and Nf is the flavor number. Our results show a decreasing of the critical coupling constant in comparison with the case of pure electromagnetic interaction, thus yielding a more favorable scenario for the occurrence of dynamical symmetry breaking. Nevertheless, the number of renormalized masses is not changed by the four-fermion interaction within our approximation. For two-dimensional materials, in application in condensed matter systems, it implies an energy gap at the Dirac points or valleys of the honeycomb lattice. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Dynamical mass generation in pseudoquantum electrodynamics with four-fermion interactions

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Dynamical mass generation in pseudoquantum electrodynamics with four-fermion interactions

Abstract

We describe dynamical symmetry breaking in a system of massless Dirac fermions with both electromagnetic and four-fermion interactions in (2+1) dimensions. The former is described by the pseudo quantum electrodynamics, and the latter is given by the so-called Gross-Neveu action. We apply the Hubbard-Stratonovich transformation and the large-Nf expansion in our model to obtain a Yukawa action. Thereafter, the presence of a symmetry broken phase is inferred from the nonperturbative Schwinger-Dyson equation for the electron propagator. This is the physical solution whenever the fine-structure constant is larger than a critical value αc(DNf). In particular, we obtain the critical coupling constant αc≈0.36 for DNf=8., where D=2, 4 corresponds to the SU(2) and SU(4) cases, respectively, and Nf is the flavor number. Our results show a decreasing of the critical coupling constant in comparison with the case of pure electromagnetic interaction, thus yielding a more favorable scenario for the occurrence of dynamical symmetry breaking. Nevertheless, the number of renormalized masses is not changed by the four-fermion interaction within our approximation. For two-dimensional materials, in application in condensed matter systems, it implies an energy gap at the Dirac points or valleys of the honeycomb lattice.
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Publisher
American Physical Society (APS)
Copyright
Copyright © © 2017 American Physical Society
ISSN
1550-7998
eISSN
1550-2368
D.O.I.
10.1103/PhysRevD.96.034005
Publisher site
See Article on Publisher Site

Abstract

We describe dynamical symmetry breaking in a system of massless Dirac fermions with both electromagnetic and four-fermion interactions in (2+1) dimensions. The former is described by the pseudo quantum electrodynamics, and the latter is given by the so-called Gross-Neveu action. We apply the Hubbard-Stratonovich transformation and the large-Nf expansion in our model to obtain a Yukawa action. Thereafter, the presence of a symmetry broken phase is inferred from the nonperturbative Schwinger-Dyson equation for the electron propagator. This is the physical solution whenever the fine-structure constant is larger than a critical value αc(DNf). In particular, we obtain the critical coupling constant αc≈0.36 for DNf=8., where D=2, 4 corresponds to the SU(2) and SU(4) cases, respectively, and Nf is the flavor number. Our results show a decreasing of the critical coupling constant in comparison with the case of pure electromagnetic interaction, thus yielding a more favorable scenario for the occurrence of dynamical symmetry breaking. Nevertheless, the number of renormalized masses is not changed by the four-fermion interaction within our approximation. For two-dimensional materials, in application in condensed matter systems, it implies an energy gap at the Dirac points or valleys of the honeycomb lattice.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Aug 1, 2017

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