Inhomogeneous Phases in the Chirally Imbalanced 2 + 1-Dimensional Gross-Neveu Model and Their Absence in the Continuum Limit

Pannullo, Laurin; Wagner, Marc; Winstel, Marc

doi:10.3390/sym14020265

Cited by 15 publications

(19 citation statements)

References 70 publications

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“…Stability of homogeneous phases against inhomogeneous perturbations in 2+1 dimensions Marc Winstel is expected to vanish in the continuum limit. We highlight that we do not observe inhomogeneous condensates on the lattice when Γ (2) ≥ 0, ∀ at given and , similar to [24,27].…”

Section: Pos(lattice2022)195supporting

confidence: 87%

“…One obtains multiple degenerate inhomogeneous minima even when neglecting the ones which are related via global (3) rotations of the vector ( (x), 4 (x), 5 (x)). Note that the bosonic fields are allowed to be functions of the two spatial coordinates x = ( 1 , 2 ), but one-dimensional functions are observed as the resulting ground state after minimization of the effective action similar to our results in the GN model [27]. We find degenerate minima, where both Σ(x) and 45 (x) oscillate.…”

Section: Pos(lattice2022)195supporting

confidence: 76%

“…4.3 of Ref. [27]). We present an exemplary plot of inhomogeneous condensates obtained at finite / ¯ 0 = 1.033 and / ¯ 0 = 0.137 using naive fermions at finite lattice spacing ¯ 0 = 0.365 in Fig.…”

Section: Pos(lattice2022)195mentioning

confidence: 90%

“…In 2 + 1 dimensions the situation seems to differ from even spacetime dimensions. Even though inhomogeneous condensates can be favored at finite regulator values in the 2 + 1-dimensional GN model (depending on the chosen regularization scheme), the inhomogeneous phase vanishes in the renormalized limit [23][24][25][26][27]. In this work, we analyze the stability of homogeneous condensates in a variety of Four-Fermion (FF) models and recover expressions similar to those derived in Ref.…”

Section: Introductionmentioning

confidence: 94%

“…Since the found inhomogeneities coincide with the region of negative Γ (2) (q ≠ 0) when evaluating the two-point functions (18) on the lattice (as in Refs. [24,27]), the observed ground states are only cutoff effects and the inhomogeneous phase Note that the naive discretization requires a weighting function with certain properties. This is, e.g., discussed in [17,24,34].…”

Section: Pos(lattice2022)195mentioning

confidence: 99%

See 4 more Smart Citations

Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions

Winstel¹,

Pannullo²

2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

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In this work, inhomogeneous chiral phases are studied in a variety of Four-Fermion and Yukawa models in 2 + 1 dimensions at zero and non-zero temperature and chemical potentials. Employing the mean-field approximation, we do not find indications for an inhomogeneous phase in any of the studied models. We show that the homogeneous phases are stable against inhomogeneous perturbations. At zero temperature, full analytic results are presented.

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Section: Pos(lattice2022)195supporting

confidence: 87%

Section: Pos(lattice2022)195supporting

confidence: 76%

Section: Pos(lattice2022)195mentioning

confidence: 90%

Section: Introductionmentioning

confidence: 94%

Section: Pos(lattice2022)195mentioning

confidence: 99%

See 3 more Smart Citations

Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions

Winstel¹,

Pannullo²

2023

Proceedings of the 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)

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Anomalies and persistent order in the chiral Gross-Neveu model

Ciccone,

Di Pietro,

Serone

2024

J. High Energ. Phys.

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We study the 2d chiral Gross-Neveu model at finite temperature T and chemical potential μ. The analysis is performed by relating the theory to a SU(N) × U(1) Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At μ = 0 we show that a certain ℤ2-valued ’t Hooft anomaly forbids the system to be trivially gapped when fermions are periodic along the thermal circle for any N and any T > 0. We also study the two-point function of a certain composite fermion operator which allows us to determine the remnants for T > 0 of the inhomogeneous chiral phase configuration found at T = 0 for any N and any μ. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for T > 0 and any μ for periodic fermions, as expected from anomaly considerations. A large N analysis confirms the above findings.

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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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Inhomogeneous Phases in the Chirally Imbalanced 2 + 1-Dimensional Gross-Neveu Model and Their Absence in the Continuum Limit

Cited by 15 publications

References 70 publications

Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions

Stability of homogeneous chiral phases against inhomogeneous perturbations in 2+1 dimensions

Anomalies and persistent order in the chiral Gross-Neveu model

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

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