Holstein-Primakoff Boson Research Articles

Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves

We propose a new scheme of modifying spin waves so as to describe the thermodynamic properties of various noncollinear antiferromagnets with particular interest in a comparison between edge- versus corner-sharing triangular-based lattices. The well-known modified spin-wave theory for collinear antiferromagnets diagonalizes a bosonic Hamiltonian subject to the constraint that the total staggered magnetization be zero. Applying this scheme to frustrated noncollinear antiferromagnets ends in a poor thermodynamics, missing the optimal ground state and breaking the local U(1) rotational symmetry. We find such a plausible double-constraint condition for spin spirals as to spontaneously go back to the traditional single-constraint condition at the onset of a collinear Néel-ordered classical ground state. We first diagonalize only the bilinear terms in Holstein-Primakoff boson operators on the order of spin magnitude S and then bring these linear spin waves into interaction in a perturbative rather than variational manner. We demonstrate specific-heat calculations in terms of thus-modified interacting spin waves on various triangular-based lattices. In zero dimension, modified-spin-wave findings in comparison with finite-temperature Lanczos calculations turn out so successful as to reproduce the monomodal and bimodal specific-heat temperature profiles of the triangular-based edge-sharing Platonic and corner-sharing Archimedean polyhedral-lattice antiferromagnets, respectively. In two dimensions, high-temperature series expansions and tensor-network-based renormalization-group calculations are still controversial especially at low temperatures, and under such circumstances, modified spin waves interestingly predict that the specific heat of the kagome-lattice antiferromagnet in the corner-sharing geometry remains having both mid-temperature broad maximum and low-temperature narrow peak in the thermodynamic limit, while the specific heat of the triangular-lattice antiferromagnet in the edge-sharing geometry retains a low-temperature sharp peak followed by a mid-temperature weak anormaly in the thermodynamic limit. By further calculating one-magnon spectral functions in terms of our newly developed double-constraint modified spin-wave theory, we reveal that not only the elaborate modification scheme but also quantum corrections, especially those caused by the O(S 0) primary self-energies, are key ingredients in the successful description of triangular-based-lattice noncollinear antiferromagnets over the whole temperature range of absolute zero to infinity.

Topological magnons on the triangular kagome lattice

We present the topology of magnons on the triangular kagome lattice (TKL) by calculating its Berry curvature, Chern number, and edge states. In addition to the ferromagnetic state, the TKL hosts ferrimagnetic ground state as its two sublattices can couple with each other either ferromagnetically or antiferromagnetically. Using Holstein-Primakoff (HP) boson theory and Green's function approach, we find that the TKL has a rich topological band structure with added high Chern numbers compared with the kagome and honeycomb lattices. The magnon edge current allows a convenient calculation of thermal Hall coefficients and the orbital angular momentum gives correlation to the Einstein--de Haas effect. We apply the calculations to the TKL and derive the topological gyromagnetic ratio showing a nonzero Einstein--de Haas effect in the zero-temperature limit. Our results render the TKL as a potential platform for quantum magnonics applications including high-precision mechanical sensors and information transmission.

Magnon damping in the zigzag phase of the Kitaev-Heisenberg- Γ model on a honeycomb lattice

We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an off-diagonal exchange $\Gamma$ and isotropic third-nearest-neighbor interaction $J_3$ on a honeycomb lattice. This model is relevant to a description of the magnetic properties of iridium oxides $\alpha$-Li$_2$IrO$_3$ and Na$_2$IrO$_3$, and Ru-based materials such as $\alpha$-RuCl$_3$. We use an unconventional parametrization of the spin-wave expansion, in which each Holstein-Primakoff boson is represented by two conjugate hermitian operators. This approach gives us an advantage over the conventional one in identifying parameter regimes where calculations can be performed analytically. Focusing on the parameter regime with the zigzag spin pattern in the ground state that is consistent with experiments, we demonstrate that one such region is $\Gamma = K>0$, where $K$ is the Kitaev coupling. Within our approach we are able to obtain explicit analytical expressions for magnon energies and eigenstates and go beyond the standard linear spin-wave theory approximation by calculating magnon damping and demonstrating its role in the dynamical structure factor. We show that the magnon damping effects in both Born and self-consistent approximations are very significant, underscoring the importance of non-linear magnon coupling in interpreting broad features in the neutron-scattering spectra.

Consideration of thermal Hall effect in undoped cuprates

A recent observation of thermal Hall effect of magnetic origin in underdoped cuprates calls for critical re-examination of low-energy magnetic dynamics in undoped antiferromagnetic compound on square lattice, where traditional, renormalized spin-wave theory was believed to work well. Using Holstein-Primakoff boson formalism, we find that magnon-based theories can lead to finite Berry curvature in the magnon band once the Dzyaloshinskii-Moriya spin interaction is taken into account explicitly, but fail to produce non-zero thermal Hall conductivity. Assuming accidental doping by impurities and magnon scattering off of such impurity sites fails to predict skew scattering at the level of Born approximation. Local formation of skyrmion defects is also found incapable of generating magnon thermal Hall effect. Turning to spinon-based scenario, we write down a simple model by adding spin-dependent diagonal hopping to the well-known {\pi}-flux model of spinons. The resulting two-band model has Chern number in the band structure, and generates thermal Hall conductivity whose magnetic field and temperature dependences mimic closely the observed thermal Hall signals. In disclaimer, there is no firm microscopic basis of this model and we do not claim to have found an explanation of the data, but given the unexpected nature of the experimental observation, it is hoped this work could serve as a first step towards reaching some level of understanding.

Stability of the wobbling motion in the triaxially deformed odd-A nucleus

In order to analyze the content of the exact solutions for particle-rotor models with both the rigid and the hydrodynamical moments of inertia (MoI), as a theoretical probe we apply the Holstein–Primakoff (HP) boson expansion method to the total angular momentum and the single-particle angular momentum . We study the competition between Coriolis force and the single-particle potential by employing the different choices of the diagonal HP boson representations for the components of and along a common coordinate axis, and along perpendicular axes. We do not find any wobbling level sequence associated with the rotation around the principal axis with the medium MoI. The staggering in the alignments of about the axis with the medium MoI is found in the limited range of I, while the vector is confined about the axis with the largest MoI.

Stability of the wobbling motion in an odd-mass nucleus and the analysis of Pr135

We apply alternative representations of Holstein-Primakoff boson expansion to the particle-rotor model as useful probes to test the stability and the physical contents of the exact solution. The diagonal representations with the total and single-particle angular momenta along the same axis (longitudinal case) and along two perpendicular axes (transverse case) are employed according to the system with rigid or hydrodynamical moments of inertia (MoI). The longitudinal case gives the normal wobbling mode for rigid MoI, but does not give a stable solution for hydrodynamical MoI. The transverse case applied for hydrodynamical MoI describes a few low spin states with reduced alignment of the total spin in the parallel direction to the single-particle spin, but these states differ from the wobbling mode which involves a quantized unit of rotational angular momentum. Employing the angular-momentum-dependent rigid MoI which is derived from the self-consistent Hartree-Fock-Bogoliubov equation together with angular momentum and particle-number constraints, we obtain good fitting not only to the energy-level scheme, but also to the electromagnetic transition rates and the mixing ratio for $^{135}\mathrm{Pr}$.

Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite size spin chains with a chiral spin ground state observed on bi-atomic Fe chains deposited on Iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya (DM) coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff (HP) boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the non-collinear nature of the classical ground state, there is a significant zero point reduction of the ground state magnetization of the spin spiral. Second, the two lowest energy spin waves are edge modes in the spin spiral state that, above a critical field the results into a collinear ferromagnetic ground state, become confined bulk modes. Third, in the spin spiral state, the spin wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Firstorder quantum phase transition in the two-mode Dicke model

The multi-mode Dicke model, which describes many atoms interacting with the multi-mode photons, has attracted much attention; it not only exhibits rich quantum phases, but also has an important application in quantum information. In this paper, we explore the ground-state properties of the two-mode Dicke model by the Holstein-Primakoff transformation and Boson expansion method, and theoretically predict a new first-order quantum phase transition. In the experiment, this quantum phase transition could be detected by measuring the mean-photon number or the atom population.

Collective modes in the loop-current-ordered phase of cuprates

Recently two branches of weakly dispersive collective modes have been discovered in underdoped cuprates by inelastic neutron scattering. Polarization analysis reveals that the modes are magnetic excitations. They are visible only for temperatures below the transition temperature to a broken symmetry phase, which was discovered earlier, and their intensity increases as temperature is further decreased. The broken symmetry phase itself has symmetries consistent with ordering of orbital current loops within a unit cell without breaking translational symmetry. In order to calculate the collective modes of such a state we add quantum terms to the Ashkin-Teller model with which the classical loop current order has been described. We derive that the mean-field ground state of the quantum model is a product over all unit cells of linear combination of the four possible classical configurations of the loop current order in each unit cell. The collective modes are calculated by using a generalized Holstein-Primakoff boson representation of orbital moment operators and lead to three branches of gapped weakly dispersive collective modes. The experimental results are consistent with the two lower-energy branches; the third mode is at a higher energy than looked for by present neutron-scattering experiments and might also be overdamped. Implications of the discovery of the collective modes are discussed.

Application of the Functional Schrödinger Picture Theory to the Holstein-Primakoff Boson Theory for Antiferromagnetic Spin Polarons in Two-Dimensional Systems of Strongly Correlated Electrons

Application of the Functional Schrödinger Picture Theory to the Holstein-Primakoff Boson Theory for Antiferromagnetic Spin Polarons in Two-Dimensional Systems of Strongly Correlated Electrons

Functional Schrödinger Representations of the Slave-Boson and the Holstein-Primakoff Boson theories for Two-Dimensional Systems of Antiferromagnetically-Correlated Electrons

Functional Schrödinger Representations of the Slave-Boson and the Holstein-Primakoff Boson theories for Two-Dimensional Systems of Antiferromagnetically-Correlated Electrons

A Note on the Two-Level Pairing Model Obeying the su(2) su(2)-Algebra: -- Re-formation in Terms of the su(1,1) su(1,1)-Algebra --

The two-level pairing model obeying the su(2) ⊗ su(2)-algebra, which was discussed in a previous paper, is re-formed in the framework of the su(1, 1) ⊗ su(1, 1)-algebra in the Schwinger boson representation. With the aid of the MYT mapping method, the Schwinger boson representation is reduced to the Holstein-Primakoff boson representation, which is expressed in terms of two kinds of bosons. Further, with the aid of the squeezed coherent state, the classical counterpart is obtained.

Algebraic description of triaxially deformed rotational bands in odd mass nuclei

An extensive application of the Holstein-Primakoff boson expansion to both single-particle angular momentum and total angular momentum provides an algebraic solution, which gives a good approximation to the exact results for the particle-rotor model with one high-j nucleon coupled to a triaxially deformed core. Two kinds of quantum numbers classify the rotational bands characteristic of the particle-rotor model and lead the selection rules for the interband and intraband transitions. The algebraic solution is compared with the experimental data for the odd mass isotopes $^{163,165,167}\mathrm{Lu}$ as testing grounds.

Finite-size scaling exponents in the interacting boson model

We investigate the finite-size scaling exponents for the critical point at the shape phase transition from U(5) (spherical) to O(6) (deformed $\gamma$-unstable) dynamical symmetries of the Interacting Boson Model, making use of the Holstein-Primakoff boson expansion and the continuous unitary transformation technique. We compute exactly the leading order correction to the ground state energy, the gap, the expectation value of the $d$-boson number in the ground state and the $E2$ transition probability from the ground state to the first excited state, and determine the corresponding finite-size scaling exponents.

Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model

We study the ground state properties of the critical Lipkin-Meshkov-Glick model. Using the Holstein-Primakoff boson representation, and the continuous unitary transformation technique, we compute explicitly the finite-size scaling exponents for the energy gap, the ground state energy, the magnetization, and the spin-spin correlation functions. Finally, we discuss the behavior of the two-spin entanglement in the vicinity of the phase transition.

On the Coupling of Two su(1,1) Spins in the Holstein-Primakoff Type Boson Representation

The su(1, 1) algebra is quite interesting, because with the help of this algebra, schematic aspects of thermal effects in many-boson and oscillating systems can be described in a conservative form. 1), 2) In addition to the above, we have another example in many-body systems. The classical and semi-classical time evolution of many-boson systems are treated in terms of squeezed boson coherent states. Such systems have been investigated by the present authors, together with Tsue and Fujiwara. 3), 4) In this case, the motion under investigation can be classified into two groups. One is classical motion and the other quantal fluctuations around the classical motion. Both can be treated formally in terms of two su(1, 1) spins. This will be demonstrated in a subsequent paper. 5) Further, in a new boson realization of the Lipkin model, 6) we can find two su(1, 1) spins. As mentioned above, we know that there exist a few systems composed of two su(1, 1) spins. Therefore, it may be interesting to investigate the coupling rule of two su(1,1) spins, because the coupling rule of su(2) spins is quite well known, but the case of su(1, 1) spins is not so familiar. The main aim of this paper is to give a general scheme for two coupled su(1, 1) spins and, further, to investigate the classical aspects. A certain part of the rule investigated in this paper will be used in a subsequent paper, 5) in which a possible interpretation is given for the decomposition of the classical and quantal fluctuation parts in the system described in terms of the squeezed state. For this purpose, in this section we breifly describe the su(1, 1) algebra as preparation for later sections. The su(1, 1) algebra consists of three operators, which we denote T±,0. These operators obey the relations

Unitary flow of the bosonized large-N Lipkin model

The flow equations describing the continuous unitary transformation which brings the Hamiltonian closer to diagonality are derived and solved exactly for the Lipkin model in the Holstein-Primakoff boson representation and for a large particle number N. The transformed Hamiltonian is diagonal in order 1/N3, extending known linear transformations to next-higher orders in the inverse particle number. This approach quite naturally allows one to preserve the tridiagonal structure of the original Lipkin Hamiltonian in the course of the transformation. Exact analytical results for the coupling functions and explicit expressions for the ground state energy and for the energy gap to the first excited state in order 1/N2 are presented and are compared with the accurate numerical values.

Boson mapping at finite temperature: An application to the thermo field dynamics

The Holstein-Primakoff boson mapping at finite temperature and in the framework of the thermo field dynamics (TFD) is applied to treat a fermion-boson Hamiltonian. The interaction between pairs of fermions and bosons is constructed in a model which allows for a condensate. The evolution of the condensate as a function of the temperature is investigated.

On the q-Boson Realization of the suq(2) and suq(1,1) Algebras

The q analogues of the Holstein-Primakoff boson realization of the su(2) and su(1,1) algebras are derived in the framework of a traditional many-body approach, Marumori-Yamamura-Tokunaga boson mapping. It is shown that the q-boson Fock space is the direct sum of the q-boson invariant subspace associated with the q-boson realizations of both algebras. The relevance of the role played by the projections on the q-boson image subspace is stressed.

Convergence of Boson Expansion Theory

When the Holstein-Primakoff (Hermitian)-type boson expansion theory is applied for nuclear structure calculations, truncation at the fourth-order expansion of the boson Hamil­ tonian is often used. The Dyson-type boson mapping has no difficulty concerning boson expansion, since the Dyson boson Hamiltonian is written in up to sixth-order boson oper­ ators, and we do not have to make any truncation of the boson expansion. In the present work, we propose a new clear-cut method to obtain the normal-ordered Holstein-Primakoff boson expansion. Using this method, we test whether or not the truncation of the boson expansion is good approximation in various cases. We show that truncation at the fourth­ order expansion of the normal-ordered Holstein-Primakoff boson Hamiltonian is a rather good approximation, but it is not sufficient for detailed analyses.