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

Koenigstein, Adrian; Pannullo, Laurin; Rechenberger, Stefan; Winstel, Marc; Steil, Martin J.

doi:10.1088/1751-8121/ac820a

Cited by 17 publications

(57 citation statements)

References 170 publications

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“…Thus, we simplify the search for inhomogeneous condensates by analyzing the stability of the homogeneous ground state ì (x) = ì Φ against inhomogeneous perturbations (see Ref. [30] for a detailed discussion and test of the method). Such an analysis was already applied in [12,13,24,31].…”

Section: Pos(lattice2022)195mentioning

confidence: 99%

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)195mentioning

confidence: 99%

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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“…We renormalize the theory, by requiring that the expectation value of 𝜎 assumes a homogeneous non-zero value, i.e., ⟨𝜎⟩ = 𝜎 0 , which is achieved by choosing an appropriate value of the coupling (see Refs. [6] for further details on the renormalization).…”

Section: Laurin Pannullomentioning

confidence: 99%

Flattening of the quantum effective potential in fermionic theories

Pannullo,

Endrodi,

G. Kovács

et al. 2023

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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We present methods to constrain fermionic condensates on the level of the path integral, which grant access to the quantum effective potential in the infinite volume limit. In the case of a spontaneously broken symmetry, this potential possesses a manifestly flat region, which is inaccessible to the standard approach on the lattice. However, by constraining the appropriate order parameters such as the chiral condensate, one is then able to probe the flat region. We demonstrate our method of constraining fermionic condensates in the 2-dimensional Gross-Neveu model, which exhibits a spontaneously broken chiral symmetry. We show how the potential flattens for increasing volume and that the flat region is dominated by inhomogeneous field configurations.

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“…1.1 depicts the so-called moat regime 6 [38] in pink as the remaining part of the conjectured chiral phase diagram. It is closely tied to the IP and can be regarded as a precursor phenomenon thereof [39]. The moat regime is characterized by a non-trivial meson dispersion relation that exhibits a minimum at a non-zero spatial momentum.…”

Section: The Moat Regimementioning

confidence: 99%

“…Then, a particle production that is peaked at a non-zero momentum should be detectable [38,[40][41][42]. 7 A recent investigation of the (1 + 1)-dimensional GN model [39] and FRG calculations of QCD [9] suggest that this regime could already exist at moderate chemical potentials and relatively high temperatures, thus covering a large portion of the phase diagram.…”

Section: The Moat Regimementioning

confidence: 99%

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Inhomogeneous phases and the Moat Regime in Nambu-Jona-Lasinio-Type models

Pannullo

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This thesis investigates exotic phases within effective models for strongly interacting matter. The focus lies on the chiral inhomogeneous phase (IP) that is characterized by a spontaneous breaking of translational symmetry and the moat regime, which is a precursor phenomenon exhibiting a non-trivial mesonic dispersion relation. These phenomena are expected to occur at non-zero baryon densities, which is a parameter region that is mostly non-accessible to first-principle investigations of Quantum chromodynamics (QCD). As an alternative approach, we consider the Gross-Neveu (GN) and Nambu-Jona-Lasinio (NJL) model within the mean-field approximation, which can be regarded as effective models for QCD. We focus on two aspects of the moat regime and the IP in these models. First, we investigate the influence of the employed regularization scheme in the (3+1)-dimensional NJL model, which is nonrenormalizable, i.e., the regulator cannot be removed. We find that the moat regime is a robust feature under change of regularization scheme, while the IP is sensitive to the specific choice of scheme. This suggests that the moat regime is a universal feature of the phase diagram of the NJL model, while the IP might only be an artifact of the employed regulator. Second, we study the influence of the number of spatial dimensions on the emergence of the IP. To this end, we investigate the GN model in noninteger spatial dimensions d. We find that the IP and the moat regime are present for d < 2, while they are absent for d > 2. This demonstrates the central role of the dimensionality of spacetime and illustrates the connection of previously obtained results in this model in integer number of spatial dimensions. Moreover, this suggests that the occurrence of these phenomena in three spatial dimensions is solely caused by the finite regulator. In summary, this thesis contributes to advancing our understanding of the phase structure of QCD, particularly regarding the existence and characteristics of inhomogeneous phases and the moat regime. Even though the investigations are performed within effective models, they provide valuable insight into the aspects that are crucial for the formation of an inhomogeneous chiral condensate in fermionic theories.

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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*

Cited by 17 publications

References 170 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

Flattening of the quantum effective potential in fermionic theories

Inhomogeneous phases and the Moat Regime in Nambu-Jona-Lasinio-Type models

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