A new skyrmion crystal

Kügler, M.; Shtrikman, S.

doi:10.1016/0370-2693(88)90653-3

Cited by 116 publications

(138 citation statements)

References 11 publications

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“…It is shown that, on a cubic lattice, any energy minimizer which satisfies a certain virial constraint of Derrick type, and is equivariant with repect to (a certain subgroup of) the lattice symmetries is automatically a soliton crystal. This result implies that, in particular, the "Skyrme crystal" found numerically by Castillejo et al [6] and Kugler and Shtrikman [15] is a soliton crystal according to our definition. Some concluding remarks are presented in section 5.…”

Section: Introductionsupporting

confidence: 73%

Solitons on Tori and Soliton Crystals

Speight

2014

Commun. Math. Phys.

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Necessary conditions for a soliton on a torus M = R m /Λ to be a soliton crystal, that is, a spatially periodic array of topological solitons in stable equilibrium, are derived. The stress tensor of the soliton must be L 2 orthogonal to E, the space of parallel symmetric bilinear forms on T M , and, further, a certain symmetric bilinear form on E, called the hessian, must be positive. It is shown that, for baby Skyrme models, the first condition actually implies the second. It is also shown that, for any choice of period lattice Λ, there is a baby Skyrme model which supports a soliton crystal of periodicity Λ. For the three-dimensional Skyrme model, it is shown that any soliton solution on a cubic lattice which satisfies a virial constraint and is equivariant with respect to (a subgroup of) the lattice symmetries automatically satisfies both tests. This verifies in particular that the celebrated Skyrme crystal of Castillejo et al., and Kugler and Shtrikman, passes both tests.

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Section: Introductionsupporting

confidence: 73%

Solitons on Tori and Soliton Crystals

Speight

2014

Commun. Math. Phys.

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“…Therefore, the asymptotic interactions could not be used to predict the Skyrme crystal lattice constant on their own: For m = 0, the lattice constant we find is a ≈ 4.71 with an energy of E ≈ 4.15 per unit cell. The values found previously are a ≈ 4.7 [18] 8 with an energy of E ≈ 4.15 per B = 4 unit cell. In the m = 1.0 case, the Skyrmion crystal was not computed before.…”

Section: The Skyrme Crystalmentioning

confidence: 55%

“…The Skyrme crystal can be thought of as an infinite simple cubic (sc) lattice of B = 4 Skyrmions, all in the same orientation (compare [18]). Although we have found that at close range, a relative rotation of 90…”

Section: The Skyrme Crystalmentioning

confidence: 99%

Interactions of B = 4 Skyrmions

Feist

2012

J. High Energ. Phys.

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It is known that the interactions of single Skyrmions are asymptotically described by a Yukawa dipole potential. Less is known about the interactions of solutions of the Skyrme model with higher baryon number. In this paper, it is shown that Yukawa multipole theory can be more generally applied to Skyrmion interactions, and in particular to the long-range dominant interactions of the B = 4 solution of the Skyrme model, which models the α-particle. A method that gives the quadrupole nature of the interaction a more intuitive meaning in the pion field colour picture is demonstrated. Numerical methods are employed to find the precise strength of quadrupole and octupole interactions. The results are applied to the B = 8 and B = 12 solutions and to the Skyrme crystal. * D. Feist@damtp.cam.ac.uk

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“…And people found that, when the skyrmions are put onto the FCC crystal at low density, in the half-skyrmion phase at high density, the crystal vertices at which half-baryons are concentrated form a cubic crystal [4,5]. The order parameter which charactorizes this phase transition is the space average of the quark-antiquark condensate qq which vanishes in the half-skyrmion phase.…”

mentioning

confidence: 99%

Mass degeneracy of heavy-light mesons with chiral partner structure in the half-Skyrmion phase

Suenaga

et al. 2015

Phys. Rev. D

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We explore the mass splitting of the heavy-light mesons with chiral partner structure in nuclear matter. In our calculation, we employed the heavy hadron chiral perturbation theory with chiral partner structure and the nuclear matter is constructed by putting skyrmions from the standard Skyrme model onto the face-centered cubic crystal and regarding the skyrmion matter as nuclear matter. We find that, although the masses of the heavy-light mesons with chiral partner structure are splitted in the matter-free space and skyrmion phase, they are degenerated in the half-skyrmion phase in which the chiral symmetry is restored globally. This observation suggests that the magnitude of the mass splitting of the heavy-light mesons with chiral partner structure can be used as a probe of the phase structure of the nuclear matter.Although the nuclear matter properties are difficult to access, it is a crucial and an interesting object to study them in both particle and nuclear physics because they are critically concerned with such issues as the equation of state (EoS) relevant to the compact-star matter and the chiral symmetry breaking/restoration in dense matter( see., e.g., Ref.[1] and references therein).Among all the approaches to the nuclear matter, skyrmion crystal is such one in which the nuclear matter properties are studied by putting skyrmions onto the crystal structure and regarding the skyrmion matter as baryonic matter [2](see also Ref.[3] and references therein). By changing the crystal size, the density effect enters. For example, in the face-centered cubic (FCC) crystal [4,5] adopted in this paper, ρ = 4/(2L) 3 with ρ and L being the nuclear matter density and crystal size, respectively. The advantage of the skyrmion crystal approach to nuclear matter is that both the nuclear matter and medium modified hadron properties can be treated in a unified way [6].In the skyrmion crystal approach, when we reduce the crystal size, or, equivalently, increase the nuclear matter density, the nuclear matter undergoes a phase transition from skyrmion phase to half-skyrmion phase in which there is a skyrmion configuration with a half baryon number at each crystal vertex [7]. And people found that, when the skyrmions are put onto the FCC crystal at low density, in the half-skyrmion phase at high density, the crystal vertices at which half-baryons are concentrated form a cubic crystal [4,5]. The order parameter which charactorizes this phase transition is the space average of the quark-antiquark condensate qq which vanishes in the half-skyrmion phase. Note that although the space average of the quark-antiquark condensate vanishes in * suenaga@hken.phys.nagoya-u.ac.jp † he@hken.phys.nagoya-u.ac.jp ‡ yongliangma@jlu.edu.cn § harada@hken.phys.nagoya-u.ac.jp the half-skyrmion phase, chiral symmetry is still locally broken since the pion decay constant in the baryonic matter f * π which charactorizes the chiral symmetry breaking does not vanish [8] and the quark-antiquark condensate is locally non-zero [9]. At this moment, properti...

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A new skyrmion crystal

Cited by 116 publications

References 11 publications

Solitons on Tori and Soliton Crystals

Solitons on Tori and Soliton Crystals

Interactions of B = 4 Skyrmions

Mass degeneracy of heavy-light mesons with chiral partner structure in the half-Skyrmion phase

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