Boson Representation Research Articles

Quantum correlation and entanglement in the Heisenberg model with biquadratic interaction on square lattice

We study the bipartite entanglement as well as the correlation content between two partitions of the quantum 2D Heisenberg model with biquadratic interactions, where the $$\theta $$ parameter controls the ratio of the biquadratic and exchange couplings. We also investigate the pairwise entanglement between nearest-neighbor qubits. The calculations were performed for the model on square lattice, in the Neel phase and ferroquadrupolar phase using spin wave theory and Schwinger boson approaches. In the Neel phase that corresponds to range $$-\pi<\theta <0$$ , we use the Dyson–Maleev representation and SU(2) Schwinger boson representation to calculate the von Neumann entropy as function of the biquadratic coupling $$J_\mathrm{{bq}}$$ . In the ferroquadrupolar phase, we use the SU(3) Schwinger boson representation which is adequate to treat this phase.

Prime Suspects in a Quantum Ladder.

In this Letter we set up a suggestive number theory interpretation of a quantum ladder system made of N coupled chains of spin 1/2. Using the hard-core boson representation and a leg-Hamiltonian made of a magnetic field and a hopping term, we can associate to the spins σ_{a} the prime numbers p_{a} so that the chains become quantum registers for square-free integers. The rung Hamiltonian involves permutation terms between next-neighbor chains and a coprime repulsive interaction. The system has various phases; in particular, there is one whose ground state is a coherent superposition of the first N prime numbers. We also discuss the realization of such a model in terms of an open quantum system with a dissipative Lindblad dynamics.

Isovector Pair Correlations of Nucleons in Nuclei

A finite boson representation of fermion operators is obtained. The collective Hamiltonian for a description of the pair excitation is constructed and the collective potential energy is analyzed. The collective modes related to the addition and removal of pair of particles are partitioned off the variety of nuclear degrees of freedom.

Bosonic representation of a Lipkin-Meshkov-Glick model with Markovian dissipation

We study the dynamics of a Lipkin-Meshkov-Glick model in the presence of Markovian dissipation, with a focus on late-time dynamics and the approach to thermal equilibrium. Making use of a vectorized bosonic representation of the corresponding Lindblad master equation, we use degenerate perturbation theory in the weak-dissipation limit to analytically obtain the eigenvalues and eigenvectors of the Liouvillian superoperator, which in turn give access to closed-form analytical expressions for the time evolution of the density operator and observables. Our approach is valid for large systems, but takes into account leading-order finite-size corrections to the infinite-system result. As an application, we show that the dissipative Lipkin-Meshkov-Glick model equilibrates by passing through a continuum of thermal states with damped oscillations superimposed, until finally reaching an equilibrium state with a temperature that in general differs from the bath temperature. We discuss limitations of our analytic techniques by comparing to exact numerical results.

Nonclassicality of photon-modulated atomic coherent states in the Schwinger bosonic realization* *Project supported by the National Natural Science Foundation of China (Grant No. 11347026) and the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2016AM03 and ZR2017MA011).

We theoretically introduce two new photon-modulated atomic coherent states (ACSs) via using the Schwinger bosonic representation of the angular momentum operators (the sequential operations ) on an ACS, and investigate their nonclassicality using the Wigner distribution, photon number distribution, and entanglement entropy. It is found that photon-modulated ACSs possess more stronger nonclassicality than the original ACS in certain regions of τ, the nonclassicality enhances with increasing number n of the operations J ± and the operation enhances the entanglement in the region of small (large) τ.

Charge instabilities of the extended attractive Hubbard model on the cubic lattice

The paramagnetic phase of the extended attractive Hubbard model on the cubic lattice is studied within the spin rotation invariant Kotliar-Ruckenstein slave boson representation at zero temperature. It is obtained that the quasiparticle residue of the Fermi liquid phase vanishes for all densities at an interaction strength slightly smaller than [Formula: see text] that signals the Brinkman–Rice transition, and that it weakly depends on density. While for vanishing non-local interaction parameters, homogeneous static charge instabilities are found in a rather narrow window centered around quarter filling and [Formula: see text], increasing them to [Formula: see text] results into a severe narrowing of this window. On the contrary, when all interaction parameters are attractive, for example for [Formula: see text], a large parameter range in which homogeneous static charge instabilities is found. Yet, this systematically happens inside the Fermi liquid phase.

On the dissipative coherent states of magnons

Research in spintronics has attracted much attention in the last few years due to the technological progress in generating and manipulating spin currents in miniaturized devices. Notwithstanding dissipative effects are inherent to experiments, in many theoretical works the damping of spin waves is included later by phenomenological arguments or even disregarded. Among the many techniques that have been used to treat magnetic models, bosonic representations is one of them. In this work, we chose the Holstein–Primakoff bosonic formalism to treat a ferromagnetic model with a priori inclusion of the damping term. Damping is included through a non-Hermitian term in the Hamiltonian and we showed that the well-known coherent state formalism can be generalized to properly represent the dissipative magnon model. The obtained results are then used to describe the precession magnetization in spintronic experiments, as the spin pumping process.

Spin transport properties of anisotropic Heisenberg antiferromagnet on honeycomb lattice in the presence of magnetic field

We have addressed the spin conductivity of a two-dimensional anisotropic antiferromagnet on honeycomb lattice in the presence of a longitudinal magnetic field. A spatial anisotropy in the form of a weak Dzyaloshinskii-Moriya interaction is considered in the model Hamiltonian. Next nearest neighbor exchange coupling has been added to the model Hamiltonian. We have investigated both dynamical and static spin conductivities in terms of the excitation spectrum by means of a hard core bosonic representation. The effects of next-nearest-neighbor coupling and the Dzyaloshinskii-Moriya interaction on the spin transport properties have also been studied via the bosonic model by a Green’s function approach. We have found the temperature dependence of static spin conductivity in the field induced gapped spin-polarized phase for various magnetic field and anisotropy parameters. Furthermore we have studied the magnetic field dependence of the static spin conductivity for various Dzyaloshinskii-Moriya interaction strength and the frequency dependence of the dynamical spin conductivity for various next nearest neighbor coupling constants. We find that the peak in the static spin conductivity moves to higher temperature upon increasing the magnetic field at fixed anisotropy parameter. The static spin conductivity is found to be monotonically decreasing with magnetic field due to increase of the energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of the spin conductivity for different magnetic field and various next nearest neighbor coupling constants.

Schubert Derivations on the Infinite Wedge Power

The Schubert derivation is a distinguished Hasse–Schmidt derivation on the exterior algebra of a free abelian group, encoding the formalism of Schubert calculus for all Grassmannians at once. The purpose of this paper is to extend the Schubert derivation to the infinite exterior power of a free $$\mathbb Z$$ -module of infinite rank (fermionic Fock space). Classical vertex operators naturally arise from the integration by parts formula, that also recovers the generating function occurring in the bosonic vertex representation of the Lie algebra $${gl_\infty (\mathbb Z)}$$ , due to Date, Jimbo, Kashiwara and Miwa (DJKM). In the present framework, the DJKM result will be interpreted as a limit case of the following general observation: the singular cohomology of the complex Grassmannian G(r, n) is an irreducible representation of the Lie algebra of $$n\times n$$ square matrices.

An equation of motion approach for the vibrational transition energies in the effective harmonic oscillator formalism: the Random phase approximation

A theory for calculating vibrational energy levels and infrared intensities is developed in the equation of motion framework at the random phase approximation level. The vibrational Hamiltonian is expanded in the harmonic oscillator ladder operators making a Hamiltonian a bosonic Hamiltonian. The excitation operator is expanded to include at most two creations and two annihilation operators making it equivalent to the random phase approximation. The method is applied for the calculation of vibrational spectral properties of two molecules. The results are found to be satisfactory, making this approach a viable option for large molecular systems. A theory for calculating vibrational energy levels and infrared intensities is developed in the equation of motion framework at the random phase approximation level. The vibrational Hamiltonian is expressed in bosonic representation. The excitation operator is expanded to include at most two creation and annihilation operators.

Lowest order perturbative approximation to vibrational coupled cluster method in bosonic representation

We propose a perturbative approximation to the vibrational coupled cluster method in bosonic representation to reduce the cost of calculating the cluster matrix elements by considering only the first order of S and $$\sigma $$ for the construction of the effective Hamiltonian $$e^\sigma e^{-S}He^Se^{-\sigma }$$ . With the systematic analysis of the results of two molecules, $$\hbox {H}_2\hbox {O}$$ and 1,1-difluoroethylene, we find that the accuracy of the transition energies with such low order approximation is comparable to the fully converged VCCM. The lowest order perturbative approximation is used to calculate the cluster matrix elements of the vibrational coupled cluster method in bosonic representation. The computational scaling for cluster matric elements is reduced from iterative N6 to non-iterative N4.

Combining Complex and Radial Slave Boson Fields within the Kotliar–Ruckenstein Representation of Correlated Impurities

AbstractThe gauge symmetry group of any slave boson representation allows to gauge away the phase of bosonic fields. One benefit of this radial field formulation is the elimination of spurious Bose condensations when saddle‐point approximation is performed. Within the Kotliar–Ruckenstein representation, three of the four bosonic fields can be radial while the last one has to remain complex. In this work, the procedure to carry out the functional integration involving constrained fermionic fields, complex bosonic fields, and radial bosonic fields is presented. The correctness of the representation is verified by exactly evaluating the partition function and the Green's function of the Hubbard model in the atomic limit.

Collective treatment of the isovector pair correlations: Boson representation

The theoretical approach to consideration of the Hamiltonian with pairing forces using a technique of the finite boson representation is developed. It is shown that a simultaneous description of the pairing vibrational state in $^{56}$Ni and the pairing rotational states with $T$=0 in the neighboring $N=Z$ nuclei is possible if the pairing Hamiltonian takes into account only isovector monopole pairing. However, the calculated energies of the pairing rotational states of $N=Z$ nuclei removed from $^{56}$Ni by 12 and more nucleons exceed significantly the experimental values. The possible reason of this discrepancy is discussed.

Boson Description of Band Crossing in Even Barium Isotopes

Properties of the states of yrast bands in even Ba isotopes are studied on the basis of the boson representation of fermion operators. The parameters of the boson Hamiltonian and the interaction between collective quadrupole bosons, positive parity bosons, and spins $${{J}^{\pi }}$$ from $${{0}^{ + }}$$ to $${{10}^{ + }}$$ are calculated microscopically. This approach describes band crossing in the yrast bands and reproduces their energies and $$B(E2)$$ within these bands up to $${{I}^{\pi }} = {{18}^{ + }}.$$

Massive conformal particles with non-Abelian charges from free U(2N,2N)-twistor dynamics: Quantization and coherent states

The inclusion of non-Abelian U(N) internal charges (other than the electric charge) into Twistor Theory is accomplished through the concept of “colored twistors” (ctwistors for short) transforming under the colored conformal symmetry U(2N,2N). In particular, we are interested in 2N-ctwistors describing colored spinless conformal massive particles with phase space U(2N,2N)∕U(2N)×U(2N). Penrose formulas for incidence relations are generalized to N>1. We propose U(2N)-gauge invariant Lagrangians for 2N-ctwistors and we quantize them through a bosonic representation, interpreting quantum states as particle–hole excitations above the ground state. The connection between the corresponding Hilbert (Fock-like with constraints) space and the carrier space of a discrete series representation of U(2N,2N) is established through a coherent state (holomorphic) representation.

The cohomology of the Grassmannian is a gln-module

The integral singular cohomology ring of the Grassmann variety parametrizing r-dimensional subspaces in the n-dimensional complex vector space is naturally an irreducible representation of the Lie algebra of all the n × n matrices with integral entries. The simplest case, r = 1, recovers the well known fact that any vector space is a module over the Lie algebra of its own endomorphisms. The other extremal case, corresponds to the bosonic vertex representation of the Lie algebra on the polynomial ring in infinitely many indeterminates, due to Date, Jimbo, Kashiwara and Miwa. In the present article we provide the structure of this irreducible representation explicitly, by means of a distinguished Hasse-Schmidt derivation on an exterior algebra, borrowed from Schubert Calculus

Spinning operators and defects in conformal field theory

We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic representation of the Lorentz group. The recipe yields the explicit structures in embedding space, and can be applied to any correlator of local operators, with or without a defect. We then focus on the two-point function of traceless symmetric primaries in the presence of a conformal defect, and explain how to compute the conformal blocks. In particular, we illustrate various techniques to generate the bulk channel blocks either from a radial expansion or by acting with differential operators on simpler seed blocks. For the defect channel, we detail a method to compute the blocks in closed form, in terms of projectors into mixed symmetry representations of the orthogonal group.

Non-Kitaev spin liquids in Kitaev materials

We point out that the Kitaev materials may not necessarily support Kitaev spin liquid. It is well-known that having a Kitaev term in the spin interaction is not the sufficient condition for the Kitaev spin liquid ground state. Many other spin liquids may be stabilized by the competing spin interactions of the systems. We thus explore the possibilities of non-Kitaev spin liquids in the honeycomb Kitaev materials. We carry out a systematic classification of gapped $\mathbb{Z}_2$ spin liquids using the Schwinger boson representation for the spin variables. The presence of strong spin-orbit coupling in the Kitaev materials brings new ingredients into the projective symmetry group classification of the non-Kitaev spin liquid. We predict the spectroscopic properties of these gapped non-Kitaev spin liquids. Moreover, among the gapped spin liquids that we discover, we identify the spin liquid whose spinon condensation leads to the magnetic Bragg peak structure of the zig-zag magnetic order that was observed in Na$_2$IrO$_3$ and $\alpha$-RuCl$_3$. We further discuss the possibility of gapped $\mathbb{Z}_2$ spin liquid and the deconfined quantum criticality from the zig-zag magnetic order to spin dimerization in pressurized $\alpha$-RuCl$_3$.

Longitudinal magnetization and specific heat of the anisotropic heisenberg antiferromagnet on honeycomb lattice

We study the effects of longitudinal magnetic field and temperature on the thermodynamic properties of two dimensional Heisenberg antiferromagnet on the honeycomb lattice in the presence of anisotropic Dzyaloshinskii-Moriya interaction and next nearest neighbor coupling exchange constant. In particular, the temperature dependence of specific heat have been investigated for various physical parameters in the model Hamiltonian. Using a hard core bosonic representation, the behavior of thermodynamic properties has been studied by means of excitation spectrum of mapped bosonic gas. The effect of Dzyaloshinskii-Moriya interaction term on thermodynamic properties has also been studied via the bosonic model by Green's function approach. Furthermore we have studied the magnetic field dependence of specific heat and magnetization for various anisotropy parameters. At low temperatures, the specific heat is found to be monotonically increasing with temperature for magnetic fields in the gapped field induced phase region. We have found the magnetic field dependence of specific heat shows a monotonic decreasing behavior for various magnetic fields due to increase of energy gap in the excitation spectrum. Also we have studied the dependence of magnetization on Dzyaloshinskii-Moriya interaction strength for different next nearest neighbor coupling constant.

Nonequilibrium quantum spin dynamics from two-particle irreducible functional integral techniques in the Schwinger boson representation

We present a non-equilibrium quantum field theory approach to the initial-state dynamics of spin models based on two-particle irreducible (2PI) functional integral techniques. It employs a mapping of spins to Schwinger bosons for arbitrary spin interactions and spin lengths. At next-to-leading order (NLO) in an expansion in the number of field components, a wide range of non-perturbative dynamical phenomena are shown to be captured, including relaxation of magnetizations in a 3D long-range interacting system with quenched disorder, different relaxation behaviour on both sides of a quantum phase transition and the crossover from relaxation to arrest of dynamics in a disordered spin chain previously shown to exhibit many-body-localization. Where applicable, we employ alternative state-of-the-art techniques and find rather good agreement with our 2PI NLO results. As our method can handle large system sizes and converges relatively quickly to its thermodynamic limit, it opens the possibility to study those phenomena in higher dimensions in regimes in which no other efficient methods exist. Furthermore, the approach to classical dynamics can be investigated as the spin length is increased.