Analytic topologically nontrivial solutions of the (
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)-dimensional 
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 gauged Skyrme model and extended duality

Avilés, Luis; Canfora, Fabrizio; Dimakis, N.; Hidalgo, Diego

doi:10.1103/physrevd.96.125005

Cited by 34 publications

(60 citation statements)

References 87 publications

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“…Time crystals are quantum systems where a crystalline structure emerges in time with no initial crystalline structure in space [1][2][3][4][5] (for the classical version of time crystals, including topologically protected systems, see [6][7][8][9][10][11]). A crystalline structure in time is related to the periodic dynamics of a system.…”

Section: Introductionmentioning

confidence: 99%

Topological time crystals

et al. 2019

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By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system. 5 Note that due to the negative effective mass m eff , the first energy band is the highest in energy. 2 New J. Phys. 21 (2019) 052003 where = ¢ J J i 2and J 2i−1 =J, which is identical to the SSH model [86]. The latter describes spinless fermions hopping on a 1D-lattice with staggered hopping amplitudes. Changing the ratio λ 1 /λ in (1), allows one to control the ratio ¢ J J . This effective Hamiltonian belongs to the BDI class of the periodic table of the topological insulators and superconductors [87] and is characterized by a  topological invariant, the winding number ν. For an infinite system with ¢ > J J ( ¢ < J J ), the system is in a topological (trivial) phase with winding number ν=1 (ν=0). For a finite system, the topological phase exhibits zero energy edge states protected by the topology of the bulk. The SSH model has been experimentally realized in quantum simulators and both the presence of edge states and the winding number have been measured [63][64][65]. Let us emphasize that the Wannier states w i (x, t) of equation (2) are localized wavepackets of the effective SSH Hamiltonian of equation (3). We then discuss how such states allow one to detect the topology of the SSH Hamiltonian. corresponding to quasi-energies closest to zero, see top panel. In the topological phase, these eigenstates have zero quasi-energy and are linear combinations of the edge states localized at the edge of time. That is, in the laboratory frame, a detector is placed close to the oscillating mirror (x≈0) and the probability density of clicking of the detector is shown versus time for different values of the ratio ¢ J J of the tunneling amplitudes in (3). This behavior is repeated with the period 2π/ω. At sωt/(2π)=1 and sωt/(2π)=40 there are edges where the eigenstate localizes if ¢ > J J 1. The results correspond to ω=0.067, λ=0.06 in (1) and are obtained within the quantum secular approach [84], see the appendix.

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Section: Introductionmentioning

confidence: 99%

Topological time crystals

et al. 2019

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“…The most difficult task is to find a good ansatz which keeps alive the non-trivial topological charge and, at the same time, allows for a crystal-like structure in the energy density without making the field equations impossible to solve analytically. It is worth to note that with the usual hedgehog ansatz in [34][35][36] (as well as in its finite density generalization [59,60]) the energy density in Eq. (3) (due to the trace on the internal indices) only depends on the Skyrmion profile.…”

Section: Beyond the Spherical Hedgehog Ansatzmentioning

confidence: 99%

“…Following the strategy of [59,60], the boundary conditions in the θ direction here will be chosen to be Dirichlet while in the r and φ directions they can be both periodic and antiperiodic. These are not the only allowed boundary conditions: however this is the simplest choice as it will be discussed in a moment.…”

Section: Skyrme Crystalsmentioning

confidence: 99%

“…The generalized hedgehog ansatz introduced in [53-58] [59][60][61] allowed the construction of the first analytic multi-Skyrmions at finite density (however, these Skyrmions at finite density do not have crystal-like structure).…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper, the methods in [59][60][61] will be generalized to construct ordered arrays of Baryonic tubes with crystalline structure living at finite density. One then observes transitions in which for fixed total topological charge, configurations with taller tubes but a smaller number of tubes are energetically favored over configurations made of a lower tubes but with a higher number of tubes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Ordered arrays of Baryonic tubes in the Skyrme model in ( $$3+1$$ 3 + 1 ) dimensions at finite density

Canfora

2018

Eur. Phys. J. C

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A consistent ansatz for the Skyrme model in (3 + 1)-dimensions which is able to reduce the complete set of Skyrme field equations to just one equation for the profile in situations in which the Baryon charge can be arbitrary large is introduced: moreover, the field equation for the profile can be solved explicitly. Such configurations describe ordered arrays of Baryonic tubes living in flat space-times at finite density. The plots of the energy density (as well as of the Baryon density) clearly show that the regions of maximal energy density have the shape of a tube: the energy density and the Baryon density depend periodically on two spatial directions while they are constant in the third spatial direction. Thus, these topologically non-trivial crystallike solutions can be intepreted as configurations in which most of the energy density and the baryon density are concentrated within tube-shaped regions. The positions of the energy-density peaks can be computed explicitly and they manifest a clear crystalline order. A non-trivial stability test is discussed.

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Magnetized Baryonic layer and a novel BPS bound in the gauged-non-linear-sigma-model-Maxwell theory in (3+1)-dimensions through Hamilton-Jacobi equation

Canfora

2023

J. High Energ. Phys.

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It is show that one can derive a novel BPS bound for the gauged Non-Linear-Sigma-Model (NLSM) Maxwell theory in (3+1) dimensions which can actually be saturated. Such novel bound is constructed using Hamilton-Jacobi equation from classical mechanics. The configurations saturating the bound represent Hadronic layers possessing both Baryonic charge and magnetic flux. However, unlike what happens in the more common situations, the topological charge which appears naturally in the BPS bound is a non-linear function of the Baryonic charge. This BPS bound can be saturated when the surface area of the layer is quantized. The far-reaching implications of these results are discussed. In particular, we determine the exact relation between the magnetic flux and the Baryonic charge as well as the critical value of the Baryonic chemical potential beyond which these configurations become thermodynamically unstable.

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Analytic topologically nontrivial solutions of the ( 3+1 )-dimensional U(1) gauged Skyrme model and extended duality

Cited by 34 publications

References 87 publications

Topological time crystals

Topological time crystals

Ordered arrays of Baryonic tubes in the Skyrme model in ( $$3+1$$ 3 + 1 ) dimensions at finite density

Magnetized Baryonic layer and a novel BPS bound in the gauged-non-linear-sigma-model-Maxwell theory in (3+1)-dimensions through Hamilton-Jacobi equation

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