Kink Crystal Research Articles

Kink crystal

We describe a one-dimensional kink crystal, which represents a collection of equal and equally localized kinks forming a lattice in the real axis. The results are analytical, original and may motivate other studies on localized structures in high energy physics.

Chiral crystallization in an external magnetic background: Chiral spiral versus real kink crystal

We study how an external magnetic field modifies the chiral phase structure of QCD, in particular the phases characterized by inhomogeneous chiral condensates. The magnetic field can be systematically incorporated into a generalized Ginzburg-Landau framework, and it turns out to induce a model independent universal coupling between the magnetic field and the axial isospin current. The resulting effect is found to be drastic especially in the chiral limit; no matter how small the magnetic intensity is, the tricritical Lifshitz point is totally washed out, and the real kink crystal is replaced by a magnetically induced chiral spiral. The current quark mass, on the other hand, has an opposite effect, protecting the chiral critical point from the magnetically induced chiral spiral. But once the magnetic intensity exceeds a critical value, the critical point no longer exists. We draw a semiquantitative conclusion that the critical point disappears for $\sqrt{eB}\geq 50$ MeV.

Spatially modulated chiral condensates

I discuss some properties of spatially dependent chiral condensates, focusing on one-dimensional modulations. After briefly introducing a generic formalism for studying inhomogeneous solutions in dense quark matter, I consider a plane-wave and a sinusoidal ansatz, and discuss the relationship between their order parameters and free energies, as well as a comparison of their dispersion relations. I then introduce a real kink crystal, and discuss its relationship with the sinusoidal ansatz by performing a Fourier analysis of this kind of solution.

Crystalline phases by an improved gradient expansion technique

We develop an innovative technique for studying inhomogeneous phases with a spontaneous broken symmetry. The method relies on the knowledge of the exact form of the free energy in the homogeneous phase and on a specific gradient expansion of the order parameter. We apply this method to quark matter at vanishing temperature and large chemical potential, which is expected to be relevant for astrophysical considerations. The method is remarkably reliable and fast as compared to performing the full numerical diagonalization of the quark Hamiltonian in momentum space, and is designed to improve the standard Ginzburg-Landau expansion close to the phase transition points. For definiteness we focus on inhomogeneous chiral symmetry breaking, accurately reproducing known results for 1D and 2D modulations and examining novel crystalline structures, as well. Consistently with previous results, we find that the energetically favored modulation is the so-called 1D real kink crystal. We propose a qualitative description of the pairing mechanism to motivate this result.

Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum \u2102PN\u2009\u2212\u20091 model

We give, for the first time, self-consistent large-N analytical solutions of inhomogeneous condensates in the quantum ℂPN − 1 model in the large-N limit. We find a map from a set of gap equations of the ℂPN − 1 model to those of the Gross-Neveu (GN) model (or the gap equation and the Bogoliubov-de Gennes equation), which enables us to find the self-consistent solutions. We find that the Higgs field of the ℂPN − 1 model is given as a zero mode of solutions of the GN model, and consequently only topologically non-trivial solutions of the GN model yield nontrivial solutions of the ℂPN − 1 model. A stable single soliton is constructed from an anti-kink of the GN model and has a broken (Higgs) phase inside its core, in which ℂPN − 1 modes are localized, with a symmetric (confining) phase outside. We further find a stable periodic soliton lattice constructed from a real kink crystal in the GN model, while the Ablowitz-Kaup-Newell-Segur hierarchy yields multiple solitons at arbitrary separations.

Non-Abelian twisted kinks in chiral Gross-Neveu model with isospin

The two-dimensional, massless Gross-Neveu model with ${N}_{c}$ colors and SU(2) isospin is studied analytically in the large ${N}_{c}$ limit. The chiral $\mathrm{SU}(2{)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2{)}_{R}$ symmetry is broken spontaneously in the vacuum. Twisted kinks connecting two arbitrary points on the vacuum manifold ${S}^{3}$ are constructed, and their properties are explored. The phase diagram as a function of temperature and baryon and isospin chemical potential is discussed, with special emphasis on inhomogeneous phases. The preferred form of the condensate is a product of the real kink crystal and the chiral spiral. Kink-kink scattering is solved, using the general solution of the multicomponent Bogoliubov--de Gennes equation recently presented by Takahashi.

Inhomogeneous chiral symmetry breaking in dense neutron-star matter

An increasing number of model results suggests that chiral symmetry is broken inhomogeneously in a certain window at intermediate densities in the QCD phase diagram. This could have significant effects on the properties of compact stars, possibly leading to new astrophysical signatures. In this contribution we discuss this idea by reviewing recent results on inhomogeneous chiral symmetry breaking under an astrophysics-oriented perspective. After introducing two commonly studied spatial modulations of the chiral condensate, the chiral density wave and the real kink crystal, we focus on their properties and their effect on the equation of state of quark matter. We also describe how these crystalline phases are affected by different elements which are required for a realistic description of a compact star, such as charge neutrality, the presence of magnetic fields, vector interactions and the interplay with color-superconductivity. Finally, we discuss possible signatures of inhomogeneous chiral symmetry breaking in the core of compact stars, considering the cases of mass-radius relations and neutrino emissivity explicitly.

Hybrid chiral condensate in the external magnetic field

We study the phase diagram of the Nambu-Jona-Lasinio model in the external magnetic field within the mean-field approximation, taking into account the inhomogeneous chiral condensate. It is shown that there appears a new type of the chiral condensate, endowed with two features of real kink crystal and dual chiral density wave, in the magnetic field. We also show that there are first order phase transitions between different inhomogeneous phases in the presence of magnetic field.

Phonons, pions, and quasi-long-range order in spatially modulated chiral condensates

We investigate low-energy fluctuations in the real kink crystal phase of dense quark matter within the Nambu--Jona-Lasinio model. The modulated chiral condensate breaks both the translational symmetry and chiral symmetry spontaneously, which leads to the appearance of phonons and pions that are dominant degrees of freedom in the infrared. Using the Ginzburg-Landau expansion near the Lifshitz point, we derive elastic free energies for phonons and pions in dependence on the temperature and chemical potential. We show that the one-dimensional modulation is destroyed by thermal fluctuations of phonons at nonzero temperature, and compute the exponent that characterizes the anisotropic algebraic decay of quasicondensate correlations at long distance. We also estimate finite-volume effects on the stability of the real kink crystal and briefly discuss the possibility of its existence in neutron stars.

Tuning Magnetotransport through a Magnetic Kink Crystal in a Chiral Helimagnet

We consider magnetotransport properties in a conducting chiral helimagnet, where the magnetic kink crystal (MKC) is formed under weak magnetic field applied perpendicular to the helical axis. The MKC behaves as a magnetic superlattice potential and results in Bragg scattering of conduction electrons. Tuning of the weak magnetic field enables us to control the size of the superlattice Brillouin zone and gives rise to a series of divergent resistivity anomalies originating from resonant Bragg scatterings. We discuss as well a nontrivial magnetic structure in the resonant states realized in the subsystem of the itinerant electrons.

Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit

Some time ago, Thies et al. showed that the Gross-Neveu model with a bare mass term possesses a kink-antikink crystalline phase. Corresponding self-consistent solutions, known earlier in polymer physics, are described by a self-isospectral pair of one-gap periodic Lame potentials with a Darboux displacement depending on the bare mass. We study an unusual supersymmetry of such a second order Lame system, and show that the associated first order Bogoliubov-de Gennes Hamiltonian possesses the own nonlinear supersymmetry. The Witten index is ascertained to be zero for both of the related exotic supersymmetric structures, each of which admits several alternatives for the choice of a grading operator. A restoration of the discrete chiral symmetry at zero value of the bare mass, when the kink-antikink crystalline condensate transforms into the kink crystal, is shown to be accompanied by structural changes in both of the supersymmetries. We find that the infinite period limit may or may not change the index. We also explain the origin of the Darboux dressing phenomenon recently observed in a non-periodic self-isospectral one-gap Poschl-Teller system, which describes kink-antikink baryons of Dashen, Hasslacher and Neveu.

Sliding conductivity of a magnetic kink crystal in a chiral helimagnet

We derive a current-driven sliding conductivity of the magnetic kink crystal (MKC) in chiral helimagnet under weak magnetic field applied perpendicular to the helical axis. For this purpose, we discuss the correlated dynamics of quantum-mechanical itinerant spins and the MKC which are coupled via the sd exchange interaction. The itinerant spins are treated as fully quantum-mechanical operators whereas the dynamics of the MKC is considered within classical Lagrangian formalism. By appropriately treating elementary excitations around the MKC state, we construct coupled equations of motion for the collective coordinates (the center-of-mass position and quasi-zero-mode coordinate) associated with the sliding motion of the MKC. By solving them, we demonstrate that the correlated dynamics is understood through a hierarchy of two time scales: Boltzmann relaxation time ${\ensuremath{\tau}}_{\text{el}}$, when a nonadiabatic spin-transfer torque appears, and Gilbert damping time ${\ensuremath{\tau}}_{\text{MKC}}$, when adiabatic spin-transfer torque comes up. As a notable consequence, we found that the terminal velocity of the sliding motion reverses its sign depending on the band-filling ratio of the conduction electron system.

Inhomogeneous condensates in the thermodynamics of the chiralNJL2model

We analyze the thermodynamical properties, at finite density and nonzero temperature, of the ($1+1$) dimensional chiral Gross-Neveu model (the ${\mathrm{NJL}}_{2}$ model), using the exact inhomogeneous (crystalline) condensate solutions to the gap equation. The continuous chiral symmetry of the model plays a crucial role, and the thermodynamics leads to a broken phase with a periodic spiral condensate, the ``chiral spiral,'' as a thermodynamically preferred limit of the more general ``twisted kink crystal'' solution of the gap equation. This situation should be contrasted with the Gross-Neveu model, which has a discrete chiral symmetry, and for which the phase diagram has a crystalline phase with a periodic kink crystal. We use a combination of analytic, numerical, and Ginzburg-Landau techniques to study various parts of the phase diagram.

Theory of spin current in chiral helimagnets

We give detailed description of the transport spin current in the chiral helimagnet. Under the static magnetic field applied perpendicular to the helical axis, the magnetic kink crystal (chiral soliton lattice) is formed. Once the kink crystal begins to move under the Galilean boost, the spin-density accumulation occurs inside each kink and there emerges periodic arrays of the induced magnetic dipoles carrying the transport spin current. The coherent motion of the kink crystal dynamically generates the spontaneous demagnetization field. To describe the kink crystal motion, we took account of not only the tangential $\ensuremath{\varphi}$ fluctuations but the longitudinal $\ensuremath{\theta}$ fluctuations around the helimagnetic configuration. Based on the collective coordinate method and the Dirac canonical formulation for the singular Lagrangian system, we derived the closed formulas for the mass, spin current, and induced magnetic-dipole moment accompanied with the kink crystal motion. To materialize the theoretical model presented here, symmetry-adapted material synthesis would be required, where the interplay of crystallographic and magnetic chirality plays a key role there.

Transport spin current driven by the moving kink crystal in a chiral helimagnet

We show that the bulk transport magnetic current is generated by the moving magnetic kink crystal (chiral soliton lattice) formed in the chiral helimagnet under the static magnetic field applied perpendicular to the helical axis. The current is caused by the nonequilibrium transport momentum with the kink mass being determined by the spin fluctuations around the kink crystal state. An emergence of the transport magnetic currents is then a consequence of the dynamical off-diagonal long range order along the helical axis. We derive an explicit formula for the inertial mass of the kink crystal and the current in the weak field limit.