Coherent State Ansatz Research Articles

Quasi discreteness analysis of a 2-dimensional Heisenberg ferromagnetic spin system with biquadratic interactions

The dynamical theory of soliton excitations in two-dimensional ferromagnets is studied by introducing a Hamiltonian that includes biquadratic interaction along with uniaxial anisotropy. To obtain a dynamical equation of motion, we use the Dyson-Maleev transformation and the coherent state ansatz. We obtain a Nonlinear Schrdinger equation by applying the multiple-scale and quasi-discreteness methods. For the more general nonintegrable case, we perform a multiple scale perturbation analysis to determine the discreteness effect on the soliton excitations. Finally, we examine modulational instability (MI) under the influence of small perturbations.

Variational theory of angulons and their rotational spectroscopy.

The angulon, a quasiparticle formed by a quantum rotor dressed by the excitations of a many-body bath, can be used to describe an impurity rotating in a fluid or solid environment. Here, we propose a coherent state ansatz in the co-rotating frame, which provides a comprehensive theoretical description of angulons. We reveal the quasiparticle properties, such as energies, quasiparticle weights, and spectral functions, and show that our ansatz yields a persistent decrease in the impurity's rotational constant due to many-body dressing, which is consistent with experimental observations. From our study, a picture of the angulon emerges as an effective spin interacting with a magnetic field that is self-consistently generated by the molecule's rotation. Moreover, we discuss rotational spectroscopy, which focuses on the response of rotating molecules to a laser perturbation in the linear response regime. Importantly, we take into account initial-state interactions that have been neglected in prior studies and reveal their impact on the excitation spectrum. To examine the angulon instability regime, we use a single-excitation ansatz and obtain results consistent with experiments, in which a broadening of spectral lines is observed while phonon wings remain highly suppressed due to initial-state interactions.

Disorder in order: Localization without randomness in a cold-atom system

We present a mapping between the Edwards model of disorder describing the motion of a single particle subject to randomly positioned static scatterers and the Bose polaron problem of a light quantum impurity interacting with a Bose-Einstein condensate (BEC) of heavy atoms. The mapping offers an experimental setting to investigate the physics of Anderson localization where, by exploiting the quantum nature of the BEC, the time evolution of the quantum impurity emulates the disorder-averaged dynamics of the Edwards model. Valid in any space dimension, the mapping can be extended to include interacting particles, arbitrary disorder, or confinement and can be generalized to study many-body localization. Moreover, the corresponding exactly solvable disorder model offers means to benchmark variational approaches used to study polaron physics. Here we illustrate the mapping by focusing on the case of an impurity interacting with a one-dimensional BEC through a contact interaction. While a simple wave function based on the expansion in the number of bath excitations misses the localization physics entirely, a coherent state Ansatz combined with a canonical transformation captures the physics of disorder and Anderson localization.

Bridging the quartet and pair pictures of isovector proton-neutron pairing

The formal implications of a quartet coherent-state ansatz for proton-neutron pairing are analyzed. Its nonlinear annihilation operators, which generalize the BCS linear quasiparticle operators, are computed in the quartetting case. Their structure is found to generate nontrivial relationships between the many-body correlation functions. The intrinsic structure of the quartet coherent state is detailed as it hints to the precise correspondence between the quartetting picture and the symmetry restored pair condensate picture for the proton-neutron pairing correlations.

Theory for self-bound states of dipolar Bose-Einstein condensates

We investigate the self-bound states of dipolar Dy condensates with the Gaussian-state ansatz which improves the conventional coherent-state ansatz with multimode squeezed coherent states. We show that the self-bound states consist of the experimentally observed self-bound liquid phase and the unobserved self-bound gas phase. The numerically obtained gas-liquid boundary is in good agreement with experimental data. Our theory also allows one to extract the real part of the three-body coupling constant of the Dy atoms from the particle number distribution of the condensates. In particular, we results show that the self-bound states are stabilized by the short-range three-body repulsion. Our study shed a different light to understand the self-bound droplets of Bose-Einstein condensates.

Real-space dynamics of attractive and repulsive polarons in Bose-Einstein condensates

We investigate the formation of a Bose polaron when a single impurity in a Bose-Einstein condensate is quenched from a non-interacting to an attractively interacting state in the vicinity of a Feshbach resonance. We use a beyond-Fr\"ohlich Hamiltonian to describe both sides of the resonance and a coherent-state variational ansatz to compute the time evolution of boson density profiles in position space. We find that on the repulsive side of the Feshbach resonance, the Bose polaron performs long-lived oscillations, which is surprising given that the two-body problem has only one bound state coupled to a continuum. They arise due to interference between multiply occupied bound states and therefore can be only found with many-body approaches such as the coherent-state ansatz. This is a distinguishing feature of the Bose polaron compared to the Fermi polaron where the bound state can be occupied only once. We derive an implicit equation for the frequency of these oscillations and show that it can be approximated by the energy of the two-body bound state. Finally, we consider an impurity introduced at non-zero velocity and find that, on the repulsive side, it is periodically slowed down or even arrested before speeding up again.

Kink-like excitations in a square lattice model of an antiferromagnetic spin system

Introducing the Holstein–Primakoff (H-P) bosonic representation of spin operators, the coherent state ansatz and the time dependent variational principle, the dynamics of the square lattice model of an antiferromagnetic system is studied. The dynamics is found to be directed by a set of coupled nonlinear partial differential equations. Employing the multiple exponential function method, soliton excitation in the system is studied. Multiwave kink soliton solutions and their interaction properties are analysed.

Localized spin excitations in an antiferromagnetic spin system with D-M interaction.

The existence of localized spin excitations and spin deviations along the site in a one-dimensional antiferromagnet with Dzyaloshinski-Moriya (D-M) interaction has been studied using quasiclassical approximation. By introducing the Holstein-Primakoff bosonic representation of spin operators, the coherent state ansatz, and the time dependent variational principle, a discrete set of coupled nonlinear partial differential equations governing the dynamics is derived. Employing the multiple-scale method, one, two and three solitary wave solutions are constructed and depicted graphically.

Localized spin excitations in a disordered antiferromagnetic chain with biquadratic interactions

Dynamical theory of soliton excitation in one dimensional antiferromagnet (AFM) is studied by a revised Hamiltonian in which biquadratic interaction is taken into account in addition to the uniaxial anisotropy and exchange energy. By using Holstein-Primakoff transformation, the coherent state ansatz and the time-dependent variational principle, we obtain a set of two coupled nonlinear partial differential equations that governs the dynamics of the system. Sine-cosine function method is used to study the complete nonlinear soliton excitation and the effect of inhomogeneity in the system. The presence of inhomogeneity is found to cause a disorder in the AFM system. Finally, the evolution of Modulational Instability (MI) is analyzed in the presence of small perturbations.

Soliton excitations and stability in a square lattice model of ferromagnetic spin system

We investigate the nature of nonlinear spin excitations in a square lattice model of ferromagnetic (FM) spin system with bilinear and biquadratic interactions. Using the coherent state ansatz combined with the Holstein–Primakoff (HP) bosonic representation of spin operators, the dynamics is found to be governed by a discrete nonlinear equation which possesses soliton solution. The modulational instability aspects of the soliton excitations are analysed for small perturbations in wave vectors.

Dromions in ([formula omitted]) dimensional ferromagnetic spin chain with bilinear and biquadratic interactions

We study the dynamics of (2+1) dimensional ferromagnetic spin chain with bilinear and biquadratic interactions by using Holstein–Primakoff (HP) representation and the coherent state ansatz. The dynamical equations of motion are obtained by using long wavelength approximation. The sine–cosine function method is used to study the complete nonlinear excitation and the effect of the different types of interactions is investigated graphically.

An integrable model of (2+1)-dimensional Heisenberg ferromagnetic spin chain and soliton excitations

We investigate the nonlinear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic (FM) spin chains with bilinear and anisotropic interactions in the semiclassical limit using the coherent state ansatz combined with the Holstein–Primakoff (HP) bosonic representation of spin operators. In the continuum limit the dynamics is found to be governed by a new integrable nonlinear Schrödinger type equation in (2+1) dimensions. The integrability of the equation is studied by constructing Lax pair of operators. The multisoliton solution is generated through the Darboux transformation. We also propose a model representing the (2+1)-dimensional inhomogeneous Heisenberg FM spin chain and the effect of inhomogeneity is understood by performing a perturbation analysis. Finally, the modulation instability aspects are discussed via analytic solutions and graphical illustrations.

Nonlinear dynamics of inhomogeneous antiferromagnetic system with Dzyaloshinski–Moriya interactions

Soliton excitation in a one-dimensional antiferromagnet with Dzyaloshinski–Moriya interaction has been studied using the Holstein–Primakoff representation, the coherent-state ansatz and the time-dependent variational principle. The dynamics is found to be governed by a set of coupled nonlinear partial differential equations. Employing the sine–cosine function method with minimal algebra, we analyse the effect of inhomogeneity in terms of soliton under perturbation and it is found that inhomogeneity causes splitting in soliton and hence a disorder in the system.

Gaffnian holonomy through the coherent state method

We analyze the effect of exchanging quasiholes described by Gaffnian quantum Hall trial state wave functions. This exchange is carried out via adiabatic transport using the recently developed coherent state Ansatz. We argue that our Ansatz is justified if the Gaffnian parent Hamiltonian has a charge gap, even though it is gapless to neutral excitations, and may therefore properly describe the adiabatic transport of Gaffnian quasiholes. For nonunitary states such as the Gaffnian, the result of adiabatic transport cannot agree with the monodromies of the conformal block wave functions, and may or may not lead to well-defined anyon statistics. Using the coherent state Ansatz, we find two unitary solutions for the statistics, one of which agrees with the statistics of the non-Abelian spin-singlet state by Ardonne and Schoutens.

Exciton condensation in cavity quantum electrodynamics

We investigate a strong coupling and half-filling Fermi–Hubbard model coupled to a cavity light field. Using a variational approach with coherent state ansatz, we identify the atom–hole pair condensation with the appearance of superradiance transition of the cavity light field. The mechanism that causes atom–hole pairs is analysed. By spin wave approximation, the phase transition at finite temperature is analysed.

Solitary magnon excitations in a one-dimensional antiferromagnet with Dzyaloshinsky–Moriyainteractions

We investigate solitary excitations in a model of a one-dimensional antiferromagnetincluding a single-ion anisotropy and a Dzyaloshinsky–Moriya antisymmetric exchangeinteraction term. We employ the Holstein–Primakoff transformation, the coherent stateansatz and the time variational principle. We obtain two partial differential equations ofmotion by using the method of multiple scales and applying perturbation theory. By sodoing, we show that the motion of the coherent amplitude must satisfy the nonlinearSchrödinger equation. We give the single-soliton solution.

Coherent states and spontaneous symmetry breaking in light-front scalar field theory

Recently developed nuclear many-body techniques provide novel results when applied to constituent quark models and to light-front scalar field theory. We show how spontaneous symmetry breaking arises and is consistent with a coherent state ansatz in a variational treatment. The kink and the kink-antikink topological features are identified and the onset of symmetry restoration is demonstrated.

Nonlinear excitations in a magnetic quantum dot array with biquadratic interaction

Magnetic quantum dots are promising candidates for applications like quantum computers and data storage devices. We investigate the nonlinear excitations in a coupled magnetic quantum dot array with biquadratic interaction. Starting from the Heisenberg Hamiltonian, which gives the interactive energy, we derive the equations of motion in the semiclassical limit using Glauber's coherent state ansatz combined with the Holstein–Primakoff bosonic representation of spin operators. The dynamics is found to be governed by a generalized nonlinear Schrödinger equation in the continuum limit. In the lower order of the expansion parameters, the system admits soliton solutions.

Nonlinear excitations in self‐assembled one‐dimensional quantum dot arrays

AbstractSelf‐assembled quantum dot arrays are modeled by one‐dimensional Heisenberg ferromagnetic spin chains. The interdot interaction is responsible for the ferromagnetic ordering. Starting from the Heisenberg Hamiltonian, using Bosonic operators coupled with Glauber's coherent state ansatz, the equation of motion is derived. In the lower order of the expansion parameters the dynamics is found to be governed by the nonlinear Schrödinger equation which admits soliton solution. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Kinks in discrete light cone quantization

We investigate non-trivial topological structures in discrete light cone quantization (DLCQ) through the example of the broken symmetry phase of the two-dimensional φ4 theory using antiperiodic boundary condition (APBC). We present evidence for degenerate ground states which is both a signature of spontaneous symmetry breaking and mandatory for the existence of kinks. Guided by a constrained variational calculation with a coherent state ansatz, we then extract the vacuum energy and kink mass and compare with classical and semi-classical results. We compare the DLCQ results for the number density of bosons in the kink state and the Fourier transform of the form factor of the kink with corresponding observables in the coherent variational kink state.