Half-skyrmion Phase Research Articles

Angular stripe phase in spin-orbital-angular-momentum coupled Bose condensates

We propose that novel superfluid with supersolid-like properties - angular stripe phase - can be realized in a pancake-like spin-1/2 Bose gas with spin-orbital-angular-momentum coupling. We predict a rich ground-state phase diagram, including the vortex-antivortex pair phase, half-skyrmion phase, and two different angular stripe phases. The stripe phases feature modulated angular density-density correlation with sizable contrast and can occupy a relatively large parameter space. The low-lying collective excitations, such as the dipole and breathing modes, show distinct behaviors in different phases. The existence of the novel stripe phase is also clearly indicated in the energetic and dynamic instabilities of collective modes near phase transitions. Our predictions of the angular stripe phase could be readily examined in current cold-atom experiments with $^{87}$Rb and $^{41}$K.

Ground-state phase diagram and excitation spectrum of a Bose-Einstein condensate with spin-orbital-angular-momentum coupling

We investigate the ground-state phase diagram and excitation spectrum of an interacting spinor Bose-Einstein condensate with spin-orbital-angular-momentum (SOAM) coupling realized in recent experiments by introducing atomic Raman transition with a pair of copropagating Laguerre-Gaussian laser beams that carry different orbital angular momenta (OAM) [Chen et al., Phys. Rev. Lett. 121, 113204 (2018) and Zhang et al., Phys. Rev. Lett. 122, 110402 (2019)]. Because of the ground-state degeneracy of the single-particle Hamiltonian at vanishing detuning, several angular-stripe phases, which are superposition of states with different angular quantum numbers, appear in the phase diagram. However, these phases normally exist at small detuning, which makes them hard to be probed in experiments. We show that for a large OAM difference of the laser beams, an asymmetric kind of angular-stripe phase can exist even at large detuning. The excitation spectra in different phases exhibit distinct features: In the angular-stripe phase there exist two gapless bands corresponding to the broken U(1) and rotational symmetries, while in the half-skyrmion phase the gapless band exhibits a roton-like structure. Our predictions of the angular-stripe phases and the low-energy excitations can be examined in recently realized BECs with SOAM coupling.

Ground state of spin-orbit coupled rotating ferromagnetic Bose-Einstein condensate in toroidal trap

Realization of spinor Bose-Einstein condensate in an optical trap has made it possible to create a variety of topological nontrivial structures, due to the vector character of the order parameter. Recently, artificial spin-orbit coupling in the spinor Bose-Einstein condensate, owing to coupling between the spin and the center-of-mass motion of the atom, provides an unprecedented opportunity to search for novel quantum states. As is well known, the potential well in the Bose-Einstein condensate is adjustable. The toroidal trap is an important model potential because of its simplicity and richness in physics. In particular, the spinor Bose-Einstein condensate under the toroidal trap has brought an ideal platform for studying fascinating properties of a superfluid, such as persistent flow and symmetry-breaking localization. For the case of the spin-orbit-coupled Bose-Einstein condensate, the previous studies of the toroidal trap mainly focused on the two-component or antiferromagnetic case. However, in the presence of a toroidal trap, there remains an open question whether the combined effects of the spin-orbit coupling and rotation can produce previously unknown types of topological excitations in the ferromagnetic Bose-Einstein condensate. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of spin-orbit coupled rotating ferromagnetic Bose-Einstein condensate in the toroidal trap. We concentrate on the effects of the spin-orbit coupling and the rotation on the ground states. The numerical results show that in the presence of a toroidal trap, the ground state structure is displayed as half-skyrmion chain with circular distribution. Adjusting the strength of spin-orbit coupling not only changes the number of half-skyrmion in the system, but also controls the symmetry of half-skyrmion with circular distribution. As the rotation frequency increases, the system undergoes the transitions from the plane wave to the half-skyrmion chain with circular distribution, and eventually developing the half-skyrmion phase of triangular lattice. Next, we examine the effect of spin-independent interaction on spin-orbit coupled rotating spinor Bose-Einstein condensate. As the spin-independent interaction increases, the topological defects in the condensate increase due to the variation of the local magnetic order. We also discuss the influence of well shape on the ground state structure. These topological structures can be detected via the time-of-flight absorption imaging technique. The spin-orbit coupled spinor Bose-Einstein condensate in the toroidal trap is an important quantum platform, which not only opens up a new avenue for exploring the exotic topological structures, but also is crucial for realizing the transitions among different ground states. This work paves the way for futureexploring the topological defects and the corresponding dynamical stability in quantum system subjected to the toroidal trap.

Magnetic field effect on nuclear matter from a Skyrmion crystal model

We explore magnetic field effects on the nuclear matter based on the skrymion crystal approach for the first time. It is found that the magnetic effect plays the role of a catalyzer for the topological phase transition (topological deformation for the skyrmion crystal configuration from the skrymion phase to half-skyrmion phase). Furthermore, we observe that in the presence of the magnetic field, the inhomogeneous chiral condensate persists both in the skyrmion and half-skyrmion phases. Explicitly, as the strength of magnetic field gets larger, the inhomogeneous chiral condensate in the skyrmion phase tends to be drastically localized, while in the half-skyrmion phase the inhomogeneity configuration is hardly affected. It also turns out that a large magnetic effect in a low density region distorts the baryon shape to an elliptic form but the crystal structure is intact. However, in a high density region, the crystal structure is strongly effected by the strong magnetic field. A possible correlation between the chiral inhomogeneity and the deformation of the skrymion configuration is also addressed. The results obtained in this paper might be realized in the deep interior of compact stars.

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

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.

Skyrmions, half-skyrmions and nucleon mass in dense baryonic matter

We explore the hadron properties in dense baryonic matter in a unified way by using a Skyrme model constructed with an effective Lagrangian which includes the ρ and ω vector mesons as hidden gauge bosons and is valid up to O(p4) in chiral expansion including the homogeneous Wess-Zumino terms. With the two input values of pion decay constant and the lowest lying vector meson mass which can be fixed in free space, all the other low energy constants in the effective Lagrangian are determined by their master formulas derived from holographic QCD models, which allows us to study the baryonic matter properties with no additional free parameters and thus without ambiguities. We find that the ω field that figures in the homogeneous Wess-Zumino term plays a crucial role in the skyrmion structure and its matter properties. The most striking and intriguing observation is that the pion decay constant that smoothly drops with increasing density in the Skyrmion phase stops decreasing at n1/2 at which the skyrmions in medium fractionize into half-skyrmions and remains nearly constant in the half-skyrmion phase. In accordance with the large Nc consideration, the baryon mass also stays non-scaling in the half-skyrmion phase. This feature is supported by the nuclear effective field theory with the parameters of the Lagrangian scaling modified at the skyrmion–half-skyrmion phase transition. Our exploration also uncovers the crucial role of the ω meson in multi-baryon systems as well as in the structure of a single skyrmion.

Dense baryonic matter in the hidden local symmetry approach: Half-skyrmions and nucleon mass

Hadron properties in dense medium are treated in a unified way in a skyrmion model constructed with an effective Lagrangian, in which the $\ensuremath{\rho}$ and $\ensuremath{\omega}$ vector mesons are introduced as hidden gauge bosons, valid up to $O({p}^{4})$ terms in chiral expansion including the homogeneous Wess-Zumino terms. All the low energy constants of the Lagrangian---apart from the pion decay constant and the vector meson mass---are fixed by the master formula derived from the relation between the five-dimensional holographic QCD and the four-dimensional hidden local symmetry Lagrangian. This Lagrangian allows one to pin down the density ${n}_{1/2}$ at which the skyrmions in medium fractionize into half-skyrmions, bringing in a drastic change in the equation of state of dense baryonic matter. We find that the $U(1)$ field that figures in the Chern-Simons term in the five-dimensional holographic QCD action or equivalently the $\ensuremath{\omega}$ field in the homogeneous Wess-Zumino term in the dimensionally reduced hidden local symmetry action plays a crucial role in the half-skyrmion phase. The importance of the $\ensuremath{\omega}$ degree of freedom may be connected to what happens in the instanton structure of elementary baryon noticed in holographic QCD. The most striking and intriguing in what is found in the model is that the pion decay constant that smoothly drops with increasing density in the skyrmion phase stops decreasing at ${n}_{1/2}$ and remains nearly constant in the half-skyrmion phase. In accordance with the large ${N}_{c}$ consideration, the baryon mass also stays nonscaling in the half-skyrmion phase. This feature which is reminiscent of the parity-doublet baryon model with a chirally invariant mass ${m}_{0}$ is supported by the nuclear effective field theory with the parameters of the Lagrangian scaling modified at the skyrmion--half-skyrmion phase transition. It also matches with one-loop renormalization group analysis based on hidden local symmetry. A link between a nonvanishing ${m}_{0}$ and the origin of nucleon mass distinctive from dynamically generated mass is suggested. We briefly discuss the possible consequences of the topology change found in this paper on the forthcoming experiments at the rare isotope beam machines under construction.

Kaons in dense half-Skyrmion matter

Dense hadronic matter at low temperature is expected to be in crystal and at high density make a transition to a {\em chirally restored but color-confined} state which is a novel phase hitherto unexplored. This phase transition is predicted in both skyrmion matter in 4D and instanton matter in 5D, the former in the form of half-skyrmions and the latter in the form of half-instantons or dyons. We predict that when $K^-$'s are embedded in this half-skyrmion or half-instanton (dyonic) matter which may be reached not far above the normal density, there arises an enhanced attraction from the soft dilaton field figuring for the trace anomaly of QCD and the Wess-Zumino term. This attraction may have relevance for a possible strong binding of anti-kaons in dense nuclear matter and for kaon condensation in neutron-star matter. Such kaon property in the half-skyrmion phase is highly non-perturbarive and may not be accessible by low-order chiral perturbation theory. Relevance of the half-skyrmion or dyonic matter to compact stars is discussed.

Dense skyrmion systems

Abstract The Skyrme model is used to investigate dense baryonic matter. Solutions of static close-packed skyrmions in arrays with fcc symmetry as well as bcc and intermediate symmetry are considered as a function of the density, and the phase transition into regular arrays of half-skyrmions is investigated. The fcc array of skyrmions has lowest energy in the condensed half-skyrmion phase but not in the uncondensed phase, in which the energy depends very little on the precise symmetry. The lowest energy, just 3.8% above the theoretical lower bound, occurs in the condensed half-skyrmion phase corresponding to the fcc array.