Twisted kink crystal in the chiral Gross-Neveu model

Basar, Goekce; Dunne, Gerald V.

doi:10.1103/physrevd.78.065022

Cited by 107 publications

(97 citation statements)

References 68 publications

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“…Other relevant analyses were also performed in the context of the GN model in 1 + 1 dimensions that allows for exact solutions (see, for instance, Refs. [17,18,19,20,21]). …”

Section: Introductionmentioning

confidence: 99%

Chiral modulations in curved space I: formalism

Flachi

Tanaka

2011

J. High Energ. Phys.

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The goal of this paper is to present a formalism that allows to handle fourfermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function regularization and supports the inclusion of inhomogeneous and anisotropic phases. One of the key points of the method is the use of a non-perturbative ansatz for the heat-kernel that returns the effective action in partially resummed form, providing a way to go beyond the approximations based on the Ginzburg-Landau expansion for the partition function. The effective action for the case of ultra-static Riemannian spacetimes with compact spatial section is discussed in general and a series representation, valid when the chemical potential satisfies a certain constraint, is derived. To see the formalism at work, we consider the case of static Einstein spaces at zero chemical potential. Although in this case we expect inhomogeneous phases to occur only as meta-stable states, the problem is complex enough and allows to illustrate how to implement numerical studies of inhomogeneous phases in curved space. Finally, we extend the formalism to include arbitrary chemical potentials and obtain the analytical continuation of the effective action in curved space.

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“…Other relevant analyses were also performed in the context of the GN model in 1 + 1 dimensions that allows for exact solutions (see, for instance, Refs. [17,18,19,20,21]). …”

Section: Introductionmentioning

confidence: 99%

Chiral modulations in curved space I: formalism

Flachi

Tanaka

2011

J. High Energ. Phys.

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“…(126) have been proposed by using a technique of the Ablowitz-Kaup-Newell-Segur hierarchy well-known in integrable systems [236]. These include a single-kink state [77,237,238], multiple kinks (kink-anti-kink and kink-polaron states) [268,240,241,242], and complex kinks and their crystalline states [243,244,245,246] as well as a single kink solution in Eq. (128).…”

Section: Jackiw-rebbi Index Theoremmentioning

confidence: 99%

Symmetry protected topological superfluid³He-B

Mizushima

Tsutsumi

Sato

et al. 2015

J. Phys.: Condens. Matter

158

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Abstract.Owing to the richness of symmetry and well-established knowledge on the bulk superfluidity, the superfluid 3 He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of 3 He in a multifaceted manner, including symmetry consideration, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological superfuidity of the 3 He-B confined in a slab geometry. The 3 He-B under a magnetic field is separated to two different sub-phases: The symmetry protected topological phase and non-topological phase. The former phase is characterized by the existence of symmetry protected Majorana fermions. The topological phase transition between them is triggered off by the spontaneous breaking of a hidden discrete symmetry. The critical field is quantitatively determined from the microscopic calculation that takes account of magnetic dipole interaction of 3 He nucleus. It is also demonstrated that odd-frequency evenparity Cooper pair amplitudes are emergent in low-lying quasiparticles. The key ingredients, symmetry protected Majorana fermions and odd-frequency pairing, bring an important consequence that the coupling of the surface states to an applied field is prohibited by the hidden discrete symmetry, while the topological phase transition with the spontaneous symmetry breaking is accompanied by anomalous enhancement and anisotropic quantum criticality of surface spin susceptibility. We also illustrate common topological features between topological crystalline superconductors and symmetry protected topological superfluids, taking UPt 3 and Rashba superconductors as examples.

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“…A path integral formulation of the problem, again with the introduction of a chemical potential that breaks translational invariance results in an inhomogenous chiral condensate [4]. References to a possible inhomogenous chiral condensate in the Schwinger model are still being discussed in the literature [5][6][7]. The problem is discussed in [8] where the author argues that the inhomogeneous chiral condensate in the Schwinger model at finite density is an artifact of the explicit breaking of translational invariance in the formalism.…”

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confidence: 99%

“…Therefore, we expect the toron variable to play a part in the analysis of the 't Hooft model in the presence of a chemical potential as discussed in [16]. The Gross-Neveu model [5,6] is different in this aspect since one does not integrate over all possible fermionic boundary conditions in the Euclidean time direction. This will be the case even if we introduce a bosonic variable to convert the four-fermi coupling into a fermion bilinear since we will have a Gaussian term for the bosonic field.…”

mentioning

confidence: 99%