Kink Excitations Research Articles

Lattice regularisation and entanglement structure of the Gross-Neveu model

We construct a Hamiltonian lattice regularisation of the N-flavour Gross-Neveu model that manifestly respects the full O(2N) symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field theory. In the context of this lattice model, the dynamical mass generation is intimately related to the Coleman-Mermin-Wagner and Lieb-Schultz-Mattis theorems. In particular, the model can be interpreted as lying at the first order phase transition line between a trivial and symmetry-protected topological (SPT) phase, which explains the degeneracy of the elementary kink excitations. We show that our Hamiltonian model can be solved analytically in the large N limit, producing the correct expression for the mass gap. Furthermore, we perform extensive numerical matrix product state simulations for N = 2, thereby recovering the emergent Lorentz symmetry and the proper non-perturbative mass gap scaling in the continuum limit. Finally, our simulations also reveal how the continuum limit manifests itself in the entanglement spectrum. As expected from conformal field theory we find two conformal towers, one tower spanned by the linear representations of O(4), corresponding to the trivial phase, and the other by the projective (i.e. spinor) representations, corresponding to the SPT phase.

Quasinormal modes in kink excitations and kink\u2013antikink interactions: a toy model

We study excitations and collisions of kinks in a scalar field theory where the potential has two minima with Z_2 symmetry. The field potential is designed to create a square well potential in the stability equation of the kink excitations. The stability equation is analogous to the Schrödinger equation, and therefore we use quantum mechanics techniques to study the system. We modify the square well potential continuously, which allows the excitation to tunnel and consequently turns the normal modes of the kink into quasinormal modes. We study the effect of this transition, leading to energy leak, on isolated kink excitations. Finally, we investigate kink–antikink collisions and the resulting scaling and fractal structure of the resonance windows considering both normal and quasinormal modes and compare the results.

Well-defined quantum soliton masses without supersymmetry

22 years ago, Rebhan and van Nieuwenhuizen showed that loop corrections to the mass of a quantum soliton depend on a choice of matching condition for the regulators of the vacuum and one-soliton sector Hamiltonians. In supersymmetric theories, regulators which preserve supersymmetry yield the correct quantum corrections, as these are dictated by supersymmetry. However, in a general theory it is not known which matching condition yields the correct mass. We use the leading term in the operator that creates the soliton to construct the regulated one-soliton sector Hamiltonian from that of the vacuum sector, providing the correct matching condition. As an application, we derive a simple formula for the one-loop mass of a kink in a large class of 1+1 dimensional scalar field theories and also, at one loop, we diagonalize the Hamiltonian which describes the kink excitations.

Domain walls and their interactions in a two-component Bose–Einstein condensate**Project supported by the National Natural Science Foundation of China (Grant No. 11775176), the Major Basic Research Program of the Natural Science Foundation of Shaanxi Province, China (Grant No. 2018KJXX-094), and the Key Innovative Research Team of Quantum Many-Body Theory and Quantum Control in Shaanxi Province, China (Grant No. 2017KCT-12).

We investigate domain wall excitations in a two-component Bose–Einstein condensate with two-body interactions and pair-transition effects. It is shown that domain wall excitations can be described exactly by kink and anti-kink excitations in each component. The domain wall solutions are given analytically, which exist with different conditions compared with the domain wall reported before. Bubble-droplet structure can be also obtained from the fundamental domain wall, and their interactions are investigated analytically. Especially, domain wall interactions demonstrate some striking particle transition dynamics. These striking transition effects make the domain wall admit quite different collision behavior, in contrast to the collision between solitons or other nonlinear waves. The collisions between kinks induce some phase shift, which makes the domain wall change greatly. Their collisions can be elastic or inelastic with proper combination of fundamental domain walls. These characters can be used to manipulate one domain wall by interacting with other ones.

Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model

The contribution of anyonic degrees of freedom emerging in the non-Abelian spin sector of a one-dimensional system of interacting fermions carrying both spin and SU(Nf) orbital degrees of freedom to the thermodynamic properties of the latter is studied based on the exact solution of the model. For sufficiently small temperatures and magnetic fields the anyons appear as zero energy modes localized at the massive kink excitations (Tsvelik 2014 Phys. Rev. Lett. 113 066401). From their quantum dimension they are identified as spin- anyons. The density of kinks (and anyons) can be controlled by an external magnetic field leading to the formation of a collective state of these anyons described by a parafermion conformal field theory for large fields. Based on the numerical analysis of the thermodynamic Bethe ansatz equations we propose a phase diagram for the anyonic modes.

Perturbed soliton and director deformation in a ferronematic liquid crystal

The nonlinear molecular deformation of the ferronematic liquid crystal in the presence of external applied magnetic field intensity is investigated in view of solitons for the director axis. The Frank’s free energy density of the nematic liquid crystal comprising the basic elastic deformations, molecular deformation associated with the nematic molecules and the suspended ferromagnetic particles and their interactions with magnetic field intensity is deduced to a sine-Gordon like equation using the classical Euler–Lagrange’s equation. Using the small angle approximation we establish the Ginzburg–Landau (GL) equation and a class of solutions are obtained. In the normal condition of large angle oscillation of the director axis, we constructed a damped sine-Gordon (sG) equation with the additional perturbation appears in the form of cosine function. The sG equation is solved using numerical simulation and kink excitations were obtained as the molecular deformation for the case of constant damping and distorted kink to a planar configuration transition as we increase the damping.

Propagation of electromagnetic solitons in an antiferromagnetic spinladder medium

The interplay of bilinear ferromagnetic coupling with antiferromagnetic rung and diagonal coupling along with the magnetic field component of the electromagnetic wave (EMW) has been studied by solving the Maxwell’s equation together with the two coupled Landau–Lifshitz nonlinear spin equations for the magnetization of the medium. The magnetization dynamics of the spin ladder under the influence of EMW is governed by a two coupled generalized derivative non-linear Schrödinger (CGDNLS) equations. We invoke the Jacobi elliptic function method to solve the CGDNLS equations and the EMW propagation assumes the forms of kink, antikink, soliton, and breather excitations. We perform numerical analysis on the static spin configurations and explored the typical chaotic spatial structures.

Integrable pair-transition-coupled nonlinear Schrödinger equations

We study integrable coupled nonlinear Schrödinger equations with pair particle transition between components. Based on exact solutions of the coupled model with attractive or repulsive interaction, we predict that some new dynamics of nonlinear excitations can exist, such as the striking transition dynamics of breathers, new excitation patterns for rogue waves, topological kink excitations, and other new stable excitation structures. In particular, we find that nonlinear wave solutions of this coupled system can be written as a linear superposition of solutions for the simplest scalar nonlinear Schrödinger equation. Possibilities to observe them are discussed in a cigar-shaped Bose-Einstein condensate with two hyperfine states. The results would enrich our knowledge on nonlinear excitations in many coupled nonlinear systems with transition coupling effects, such as multimode nonlinear fibers, coupled waveguides, and a multicomponent Bose-Einstein condensate system.

Truncated conformal space approach for 2D Landau–Ginzburg theories

We study the spectrum of Landau–Ginzburg theories in 1 + 1 dimensions using the truncated conformal space approach employing a compactified boson. We study these theories both in their broken and unbroken phases. We first demonstrate that we can reproduce the expected spectrum of a Φ2 theory (i.e. a free massive boson) in this framework. We then turn to Φ4 in its unbroken phase and compare our numerical results with the predictions of two-loop perturbation theory, finding excellent agreement. We then analyze the broken phase of Φ4 where kink excitations together with their bound states are present. We confirm the semiclassical predictions for this model on the number of stable kink-antikink bound states. We also test the semiclassics in the double well phase of Φ6 Landau–Ginzburg theory, again finding agreement.

Kink confinement and supersymmetry

We analyze non-integrable deformations of two-dimensional N=1 supersymmetric quantum field theories with kink excitations. As example, we consider the multi-frequency Super Sine Gordon model. At weak coupling, this model is robust with respect to kink confinement phenomena, in contrast to the purely bosonic case. If we vary the coupling, the model presents a sequence of phase transitions, where pairs of kinks disappear from the spectrum. The phase transitions fall into two classes: the first presents the critical behaviors of the Tricritical Ising model, the second instead those of the gaussian model. In the first case, close to the critical point, the model has metastable vacua, with a spontaneously supersymmetry breaking. When the life-time of the metastable vacua is sufficiently long, the role of goldstino is given by the massless Majorana fermion of the Ising model. On the contrary, supersymmetry remains exact in the phase transition of the second type.

Neutral bound states in kink-like theories

In this paper we present an elementary derivation of the semi-classical spectrum of neutral particles in a field theory with kink excitations. In the non-integrable cases, we show that each vacuum state cannot generically support more than two stable particles, since all other neutral exitations are resonances, which will eventually decay. A phase space estimate of these decay rates is also given. This shows that there may be a window of values of the coupling constant where a particle with higher mass is more stable than the one with lower mass. We also discuss the crossing symmetry properties of the semiclassical form factors and the possibility of extracting the elastic part of the kink S-matrix below their inelastic threshold. We present the analysis of theories with symmetric and asymmetric wells, as well as of those with symmetric or asymmetric kinks. Illustrative examples of such theories are provided, among others, by the tricritical Ising model, the double sine-Gordon model and by a class of potentials recently introduced by Bazeia et al.

SEMICLASSICAL METHODS IN 2D QFT: SPECTRA AND FINITE-SIZE EFFECTS

We review some recent results obtained in the analysis of two-dimensional quantum field theories by means of semiclassical techniques, which generalize methods introduced during the '70s by Dashen, Hasllacher and Neveu and by Goldstone and Jackiw. The approach is best suited to deal with quantum field theories characterized by a nonlinear interaction potential with different degenerate minima, that generates kink excitations of large mass in the small coupling regime. Under these circumstances, although the results obtained are based on a small coupling assumption, they are nevertheless nonperturbative, since the kink backgrounds around which the semiclassical expansion is performed are nonperturbative too. We will discuss the efficacy of the semiclassical method as a tool to control analytically spectrum and finite-size effects in these theories.

Nonlinear Dynamics of Microtubules: Biophysical Implications

A recently developed model of nonlinear dynamics for microtubules is further expanded based on the biophysical arguments involving the secondary structure of the constitutive protein tubulin and on the ferroelectric properties of microtubules. It is demonstrated that kink excitations arise due to GTP hydrolysis that causes a dynamical transition in the structure of tubulin. The presence of an intrinsic electric field associated with the structure of a microtubule leads to unidirectional propagation of the kink excitation along the microtubule axis. This mechanism offers an explanation of the dynamic instability phenomenon in terms of the electric field effects. Moreover, a possible elucidation of the unidirectional transport of cargo via motor proteins such as kinesin and dynein is proposed within the model developed in this paper.

Activated dynamics of semiflexible polymers on structured substrates

We study the thermally activated motion of semiflexible polymers in double-well potentials using field-theoretic methods. Shape, energy, and effective diffusion constant of kink excitations are calculated, and their dependence on the bending rigidity of the semiflexible polymer is determined. For symmetric potentials, the kink motion is purely diffusive whereas kink motion becomes directed in the presence of a driving force. We determine the average velocity of the semiflexible polymer based on the kink dynamics. The Kramers escape over the potential barriers proceeds by nucleation and diffusive motion of kink-antikink pairs, the relaxation to the straight configuration by annihilation of kink-antikink pairs. We consider both uniform and point-like driving forces. For the case of point-like forces the polymer crosses the potential barrier only if the force exceeds a critical value. Our results apply to the activated motion of biopolymers such as DNA and actin filaments or of synthetic polyelectrolytes on structured substrates.

Semiclassical particle spectrum of double sine-Gordon model

We present new theoretical results on the spectrum of the quantum field theory of the double sine-Gordon model. This non-integrable model displays different varieties of kink excitations and bound states thereof. Their mass can be obtained by using a semiclassical expression of the matrix elements of the local fields. In certain regions of the coupling-constants space the semiclassical method provides a picture which is complementary to the one of the form factor perturbation theory, since the two techniques give information about the mass of different types of excitations. In other regions the two methods are comparable, since they describe the same kind of particles. Furthermore, the semiclassical picture is particularly suited to describe the phenomenon of false vacuum decay, and it also accounts in a natural way the presence of resonance states and the occurrence of a phase transition.

Field theoretical study of a spin-1/2 ladder with unequal chain exchanges

We study the low-energy properties of a Heisenberg spin-1/2 zigzag ladder with different exchange constants on the two chains. Using a nonlinear \ensuremath{\sigma}-model field theory and Abelian bosonization, we find that the excitations are gapless, with a finite spin-wave velocity, if the values of the chain exchanges are small. If the chain exchanges are large, the system is gapped, and the energy spectra of the kink and antikink excitations are different from each other.

Nonglassy relaxation by double kinks inYBa2Cu3O7−δwith columnar defects

We present long-term relaxation measurements of the irreversible magnetization in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystals with columnar defects. Within the single vortex pinning regime we find a nonglassy response at intermediate currents, in between the half loops and superkinks glassy regimes. We demonstrate that such behavior is due to double kink excitations whose critical nucleus has a size independent of current, and occur even in the presence of pinning energy dispersion.

Mössbauer effect as a possible tool in detecting nonlinear excitations in microtubules

We investigate the electronic degrees of freedom in cytoskeletal microtubules in the continuum approximation. The equations of motion of the propagating local conformational state are solved in the low temperature regime. The solution, which is a kink excitation, is coupled to the motion of the mobile electron of the constituent tubulin. We calculate the influence of kink excitations on the probability of the M\"ossbauer emission of \ensuremath{\gamma}-active nuclei. A discussion follows on this potentially useful experimental tool for the detection of nonlinear excitations in a microtubule.

Theory of kink and domain-wall excitations in translationally invariant lattices with quartic anharmonicity

A theoretical investigation has been made of localized excitations having the form of kinks or domain walls in translationally invariant monatomic lattices with harmonic and quartic anharmonic interactions between nearest-neighbor atoms. Antisymmetric kinks are found for negative values of the anharmonic coefficient. Symmetric kinks are found to be poorly defined for translationally invariant anharmonic potentials. In the case of domain walls, stable solutions were obtained only for negative values of the anharmonic coefficient. These results are compared with those for on-site quartic anharmonicity.

EXPERIMENTAL STUDY OF THE SOLITONS IN NONLINEAR DIATOMIC MACRO-LATTICE

For a one-dimensional damped and parametrically driven diatomic-like macro-pendulum lattice, five types of the lower cutoff and upper cutoff stable soliton and kink excitations have been observed. Especially, the gap soliton which has been studied widely in physics is first observed in macro-experiments. The experimental results can be well explained qualitatively by a nonlinear Schrödinger theory after neglecting the nonuniformity effects of the pendulums.