Beyond integrability: Baryon-baryon backward scattering in the massive Gross-Neveu model

Thies, Michael

doi:10.1103/physrevd.96.076012

Cited by 4 publications

(5 citation statements)

References 20 publications

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“…The U(N) symmetry group can be further decomposed into a so-called phase symmetry, elements of U(1), and a flavor symmetry group, elements of SU(N). The phase symmetry leads to conservation of the baryon number density ψγ 2 ψ/N that is tuned by the chemical potential μ for the fermions [82][83][84][85]. On the other hand, the flavor symmetry group leads to the conservation of a vector current.…”

Section: The Gross-neveu Modelmentioning

confidence: 99%

Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (1 + 1)-dimensional Gross–Neveu model in the mean-field approximation*

Koenigstein¹,

Pannullo²,

Rechenberger³

et al. 2022

J. Phys. A: Math. Theor.

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The phase diagram of the (1 + 1)-dimensional Gross-Neveu model is reanalyzed for (non-)zero chemical potential and (non-)zero temperature within the mean-ﬁeld approximation. By investigating the momentum dependence of the bosonic two-point function, the well-known second-order phase transition from the ℤ2 symmetric phase to the so-called inhomogeneous phase is detected. In the latter phase the chiral condensate is periodically varying in space and translational invariance is broken. This work is a proof of concept study that conﬁrms that it is possible to correctly localize second-order phase transition lines between phases without condensation and phases of spatially inhomogeneous condensation via a stability analysis of the homogeneous phase. To complement other works relying on this technique, the stability analysis is explained in detail and its limitations and successes are discussed in context of the Gross-Neveu model. Additionally, we present explicit results for the bosonic wave-function renormalization in the mean-ﬁeld approximation, which is extracted analytically from the bosonic two-point function. We ﬁnd regions – a so-called moat regime – where the wave function renormalization is negative accompanying the inhomogeneous phase as expected.

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Section: The Gross-neveu Modelmentioning

confidence: 99%

Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (1 + 1)-dimensional Gross–Neveu model in the mean-field approximation*

Koenigstein¹,

Pannullo²,

Rechenberger³

et al. 2022

J. Phys. A: Math. Theor.

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“…The Z 2 symmetry is called discrete chiral symmetry. The U (1) symmetry is called phase symmetry and leads to a conserved Noether-charge density ψ γ 2 ψ, which is usually called Baryon number density [82,[96][97][98]. 6 It can be shown, see App.…”

Section: A In Vacuummentioning

confidence: 99%

Bosonic fluctuations in the $( 1 + 1 )$-dimensional Gross-Neveu(-Yukawa) model at varying $μ$ and $T$ and finite $N$

Stoll,

Zorbach,

Koenigstein

et al. 2021

Preprint

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Using analogies between flow equations from the Functional Renormalization Group and flow equations from (numerical) fluid dynamics we investigate the effects of bosonic fluctuations in a bosonized Gross-Neveu model -namely the Gross-Neveu-Yukawa model. We study this model for finite numbers of fermions at varying chemical potential and temperature in the local potential approximation. Thereby we numerically demonstrate that for any finite number of fermions and as long as the temperature is non-zero, there is no Z2 symmetry breaking for arbitrary chemical potentials.

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“…Unlike in the GN model, only the LO Lagrangian is available in the no-sea effective theory. Therefore it is sufficient to also work out the non-relativistic reduction to LO only (no "fine structure" corrections [8]). Starting point is the Dirac-TDHF equation (3).…”

Section: Non-relativistic Reduction Of the Dirac Equationmentioning

confidence: 99%

“…To reproduce the result of Ref. [8] for the non-chiral GN model, one can just set P = 0 in Eq. (21) and get a similar equation, but with a coupling constant differing by a factor of 2.…”

Section: Non-relativistic Reduction Of the Dirac Equationmentioning

confidence: 99%

“…This does not work anymore for time dependent problems, like breathers or baryon-baryon scattering [7]. Recently, time dependence was studied near the non-relativistic limit [8], using a microscopic "no-sea" effective theory where negative energy states are projected out [9]. It was found that to leading order in the non-relativistic expansion, the massive * michael.thies@gravity.fau.de GN model remains integrable with only forward elastic scattering.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Untwisting twisted NJL2 kinks by a bare fermion mass

Thies

2017

Phys. Rev. D

Self Cite

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Twisted kinks in the massless NJL2 model interpolate between two distinct vacua on the chiral circle. If one approaches the chiral limit from finite bare fermion masses m0, the vacuum is unique and twist cannot exist. This issue is studied analytically in the non-relativistic limit, using a no-sea effective theory. We conclude that even in the massless limit, the interpretation of the twisted kink has to be revised. One has to attribute the fermion number of the valence state to the twisted kink. Fermion density is spread out over the whole space due to the massless pion field. The result can be pictured as a composite of a twisted kink (carrying energy, but no fermion number) and a partial winding of the chiral spiral (carrying fermion number, but no energy). This solves at the same time the puzzle of missing baryons with fermion number N f < N in the massless NJL2 model.

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Beyond integrability: Baryon-baryon backward scattering in the massive Gross-Neveu model

Cited by 4 publications

References 20 publications

Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (1 + 1)-dimensional Gross–Neveu model in the mean-field approximation*

Detecting inhomogeneous chiral condensation from the bosonic two-point function in the (1 + 1)-dimensional Gross–Neveu model in the mean-field approximation*

Bosonic fluctuations in the $( 1 + 1 )$-dimensional Gross-Neveu(-Yukawa) model at varying $μ$ and $T$ and finite $N$

Untwisting twisted NJL2 kinks by a bare fermion mass

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