Modified Spin Wave Theory Research Articles

Kinematic interaction and condensation factor in two-dimensional quantum Heisenberg ferromagnet

We investigate the influences of Dyson’s kinematic and dynamic interaction on the physical properties of two-dimensional quantum Heisenberg ferromagnet with O(3) rotational symmetry. It is found that the repulsive potential led by dynamic interaction modifies the third large term with $$T^{3}$$ in the low-temperature series of specific heat. Under mean-field approximation, the kinematic interaction transforms the occupation-number configuration into a coherent-state configuration and significantly improves the result of modified spin wave theory in the high-temperature limit. In the low-temperature limit, the kinematic-interaction contribution to specific heat is negligibly small. For finite-size systems, it is found that a crossover temperature can be used to characterize the transition to a single-domain-type magnet. In the thermodynamic limit, the condensation factor (the number of zero-mode magnons) dominates the isothermal compressibility of magnon gas although there is not a real phase transition at finite temperatures. The asymptotic behavior of static structure factor depends on the relative size of the spin-wave wavelength with respect to the correlation length.

Thermodynamics of a delta chain with ferromagnetic and antiferromagnetic interactions

Motivated by a novel cyclic compound $Fe_{10}Gd_{10}$ with record ground state spin in which the arrangement of magnetic ions with $s=\frac{5}{2}$ and $s=\frac{7}{2}$ corresponds to a saw-tooth chain we investigate the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions. We study both classical and quantum versions of the model. The classical model is exactly solved and quantum effects are studied using full diagonalization and a finite temperature Lanczos technique for finite delta-chains as well as modified spin wave theory. It is shown that the main features of the magnetic susceptibility of the quantum spin delta chain are correctly described by the classical spin model, while quantum effects significantly change the low-temperature behavior of the specific heat. The relation of the obtained results to the $Fe_{10}Gd_{10}$ system is discussed.

Notes on Ground-State Properties of Mixed Spin-1 and Spin-1/2 Lieb-Lattice Heisenberg Antiferromagnets

Quantum Monte Carlo (QMC) simulations are performed to study ground-state properties of a mixed spin-1 and spin-1/2 Lieb-lattice Heisenberg antiferromagnet, in order to get further insight beyond the modified spin-wave (MSW) study reported in [J. Phys. Soc. Jpn. 86, 014002 (2017)]. It is confirmed that the MSW results are in good agreement with the QMC results. In particular, the scaling relation found in the MSW study, which argues that sublattice spin reductions are inversely proportional to the sublattice sizes, is observed in our QMC simulation. We present a rigorous proof for spontaneous sublattice magnetizations induced by an infinitesimal uniform magnetic field. The calculation process in the MSW theory is reexamined to clarify the mathematical structure behind the scaling relation for sublattice long-range orders.

Entanglement in the quantum one-dimensional integer spin S Heisenberg antiferromagnet

We use the modified spin wave theory of Takahashi to study the entanglement entropy in the quantum one-dimensional integer spin Heisenberg antiferromagnet. We calculate the entanglement entropy of this spin system that is well known to be a quantum wire, in the classical limit (N→∞). We obtain a decreasing the entanglement entropy with the temperature and we obtain none change in the entanglement in the point Δ=1 at T=0 where the system presents a quantum phase transition from a gapless phase in the spectrum Δ<1 to a gapped phase Δ≥1.

Anisotropic easy axis S=1 antiferromagnetic Heisenberg model with competitive interaction on a square lattice

Using a modified spin wave theory, we study the two-dimensional spin S=1 Heisenberg antiferromagnet with both spin and spatial anisotropies and competitive next-nearest neighbor interaction J2, at zero temperature. The magnetization as a function of J2 shows the existence of three different phases namely, ordered Néel, disordered and ordered collinear phases. The existence of the disordered phase depends on the values of the anisotropy parameters. The model shows a very rich phase diagram.

The magnetic properties of a quasi-two-dimensional spin 1 easy axis Heisenberg antiferromagnet with competing interactions

The Neel and collinear ordered phases of the two-dimensional S=1 antiferromagnet with next and next near neighbor exchange interactions and easy axis single ion anisotropy, on the square lattice, are studied at low temperature using a Modified Spin Wave Theory. We calculate the low-temperature quantities as a function of the temperature, frustration and anisotropy. We calculate also the phase diagram at T=0. We found a disordered phase separating the Neel and collinear phases.

Spin transport of the quantum integer spin S one-dimensional Heisenberg antiferromagnet coupled to phonons

We study the effect of the spin-phonon coupling on spin transport in the S = 1 one-dimensional Heisenberg antiferromagnet. The spin conductivity is calculated using the modified spin wave theory and the Kubo formalism of transport. We calculate the regular part of the spin conductivity, σ reg (ω), as function of the frequency at finite temperature. We obtain a strong effect of the magnon-phonon interaction on magnon transport.

Spin dynamics of aJ1−J2antiferromagnet and its implications for iron pnictides

Motivated by the recent observation of antiferromagnetic correlations in the paramagnetic phase of iron pnictides, we study the finite-temperature spin dynamics of a two-dimensional ${J}_{1}\ensuremath{-}{J}_{2}$ antiferromagnet. We consider the paramagnetic phase in the regime of a $(\ensuremath{\pi},0)$ collinear ground state, using the modified spin wave theory. Below the mean-field Ising transition temperature, we identify short-range anisotropic antiferromagnetic correlations. We show that the dynamical structure factor $\mathcal{S}(\mathbf{q},\ensuremath{\omega})$ contains elliptic features in the momentum space, and determine its variation with temperature and energy. Implications for the spin-dynamical experiments in the iron pnictides are discussed.

Modified spin-wave theory with ordering vector optimization: spatially anisotropic triangular lattice and J1J2J3 model with Heisenberg interactions

We study the ground-state phases of the S=1/2 Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice (SATL) and on the square lattice with up to next-next-nearest-neighbor coupling (the J1J2J3 model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that the MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular, collinear magnetic order is promoted at the expense of non-collinear (spiral) order, and several spiral states that are stable at the classical level disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which the MSW theory breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the SATL, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains. This shows that the MSW theory is—despite its apparent simplicity—a versatile tool for finding candidate regions in the case of spin-liquid phases, which are among prime targets for relevant quantum simulations.

Modified spin-wave theory with ordering vector optimization: frustrated bosons on the spatially anisotropic triangular lattice

We investigate a system of frustrated hardcore bosons, modeled by an XY antiferromagnet on the spatially anisotropic triangular lattice, using Takahashi's modified spin-wave (MSW) theory. In particular, we implement ordering vector optimization on the ordered reference state of MSW theory, which leads to significant improvement of the theory and accounts for quantum corrections to the classically ordered state. The MSW results at zero temperature compare favorably to exact diagonalization (ED) and projected entangled-pair state (PEPS) calculations. The resulting zero-temperature phase diagram includes a one-dimensional (1D) quasi-ordered phase, a 2D Néel ordered phase and a 2D spiraling ordered phase. Strong indications coming from the ED and PEPS calculations, as well as from the breakdown of MSW theory, suggest that the various ordered or quasi-ordered phases are separated by spin-liquid phases with short-range correlations, in analogy to what has been predicted for the Heisenberg model on the same lattice. Within MSW theory, we also explore the finite-temperature phase diagram. In agreement with the Berezinskii–Kosterlitz–Thouless (BKT) theory, we find that zero-temperature long-range-ordered phases turn into quasi-ordered phases (up to a BKT transition temperature), while zero-temperature quasi-ordered phases become short-range correlated at finite temperature. These results show that, despite its simplicity, MSW theory is very well suited to describing ordered and quasi-ordered phases of frustrated XY spins (or, equivalently, of frustrated lattice bosons) both at zero and finite temperatures. While MSW theory, just as other theoretical methods, cannot describe spin-liquid phases, its breakdown provides a fast and reliable method for singling out Hamiltonians that may feature these intriguing quantum phases. We thus suggest a tool for guiding our search for interesting systems whose properties are necessarily studied with a physical quantum simulator instead of theoretical methods.

Heat transport in low-dimensional Heisenberg antiferromagnets

In this paper we study thermal transport in the one-dimensional spin S=1 and the two dimensional spin S=1/2 Heisenberg antiferromagnets, using the modified spin wave theory and the Kubo linear response formalism, to calculate the thermal conductivity. The low-temperature thermal Drude weights, in both cases, are non-zero at finite temperature indicating a ballistic behavior.

Three-magnon process in the one-dimensional integer spin [formula omitted] antiferromagnetic Heisenberg chain

We present a calculation of the correlation function in time for the integer spin S one-dimensional antiferromagnet taking into account three-magnon process. The procedure includes two-magnon and three-magnon processes in the dynamic structure factor using a modified spin wave theory. We show that the inclusion of the three-magnon process does not change the double peak structure obtained for the Dynamical Structure Factor.

Dynamics of the quantum integer spinS one-dimensional Heisenberg antiferromagnet coupled to phonons

We present the low-temperature dynamic properties of the quantumone-dimensional Heisenberg antiferromagnet with integer spinS coupled to phonons. The calculation of the relaxation function is performedusing the combination of the memory function formalism with the modifiedspin-wave theory. The procedure includes up to two-magnon and magnon–phononprocesses. We show that the phonon–magnon coupling smooths the double-peakstructure obtained for the model in the absence of phonons, when the wavevectorq movesfrom q = π.

Spin dynamics of the frustrated integer spin antiferromagnetic Heisenberg chain

We present low-temperature static and dynamic properties of the quantumone-dimensional isotropic integer spin Heisenberg magnet with antiferromagneticnearest-neighbour (nn) and next-nearest-neighbour (nnn) interactions. The modifiedspin-wave theory is used to provide quantities such as the spin-wave dispersionrelation, the ground-state energy, the gap and its dependence with temperature,and the asymptotic behaviour of the spin–spin correlation function. The groundstate energy and the singlet–triplet energy gap are obtained for several values ofj, defined as the ratio of the nnn interaction constant to the nn one. Ourresults show that the ground-state and the gap energies increase withj, in accordance with numerical results available in the literature. The calculation of the dynamiccorrelation function is performed using the projection operator formalism: the procedure includesup to two-magnon processes. We show that, depending on the values of the frustration parameterj, the wavevector and the temperature, a double-peak structure for the dynamicalcorrelation function can develop.

Modified spin-wave theory for the S = 1 frustrated antiferromagnetic Heisenberg chain

We study the one-dimensional isotropic spin-1 Heisenberg magnet with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions by using the modified spin wave theory (MSWT). The ground state energy and the singlet-triplet energy gap are obtained for several values of j, defined as the ratio of the nnn interaction constant to the nn one. We also compare two different ways of implementing the MSWT currently found in the literature, and show that, despite the remarkable differences between the equations to be solved in each procedure, the results given by both are equivalent, except for the predicted value of the jmax, the maximum value of j accessible in each treatment. Here, we suggest that jmax is related to the disorder point of the first kind. Our results show that the ground state and the gap energies increase with j, for j ≤jmax, in accordance to previous numerical results.

Thermodynamics of spin-1∕2antiferromagnet-antiferromagnet-ferromagnet and ferromagnet-ferromagnet-antiferromagnet trimerized quantum Heisenberg chains

The magnetization process, the susceptibility and the specific heat of the spin-1/2 AF-AF-F and F-F-AF trimerized quantum Heisenberg chains have been investigated by means of the transfer matrix renormalization group (TMRG) technique as well as the modified spin-wave (MSW) theory. A magnetization plateau at $m=1/6$ for both trimerized chains is observed at low temperature. The susceptibility and the specific heat show various behaviors for different ferromagnetic and antiferromagnetic interactions and in different magnetic fields. The TMRG results of susceptibility and the specific heat can be nicely fitted by a linear superposition of double two-level systems, where two fitting equations are proposed. Three branch excitations, one gapless excitation and two gapful excitations, for both systems are found within the MSW theory. It is observed that the MSW theory captures the main characteristics of the thermodynamic behaviors at low temperatures. The TMRG results are also compared with the possible experimental data.

Quantum versus classical behavior in the boundary susceptibility of the ferromagnetic Heisenberg chain

We calculate the temperature dependence of the boundary susceptibility ${\ensuremath{\chi}}_{B}$ for the quantum ferromagnetic Heisenberg chain by a modified spin-wave theory (MSWT). We find that ${\ensuremath{\chi}}_{B}$ diverges at low temperatures $\ensuremath{\sim}\ensuremath{-}{T}^{\ensuremath{-}3}$ and therefore more rapidly and with opposite sign than the bulk susceptibility ${\ensuremath{\chi}}_{\mathrm{bulk}}\ensuremath{\sim}{T}^{\ensuremath{-}2}$. Our result for ${\ensuremath{\chi}}_{B}$ is identical in leading order with the result for the classical system. In next leading orders, however, quantum corrections to the classical result exist which are important to obtain a good description over a wide temperature range. For the $S=1∕2$ case, we show that our full result from MSWT is in excellent agreement with numerical data obtained by the density-matrix renormalization group applied to transfer matrices. Finally, we discuss the quantum to classical crossover as well as consequences of our results for experiment in some detail.

Thermodynamic properties of ferrimagnetic spin chains in the presence of a magnetic field

We have implemented three approaches to describe the thermodynamic properties of ferrimagnetic ($S=5/2, s=2$) spin chains. The application of cumulant expansion has been generalized to the ferrimagnetic chain in the presence of an external magnetic field. Using cumulants, we have obtained the field dependent effective Hamiltonian in terms of the classical variables up to the second order of quantum corrections. Thermodynamic functions, the internal energy, the specific heat and the magnetic susceptibility are obtained from the effective Hamiltonian. We have also examined the modified spin wave theory to derive the same physical properties. Finally, we have studied our model using quantum Monte Carlo simulation to obtain accurate results. The comparison of the above results and also the high temperature series expansion shows that cumulant expansion gives good results for moderate and high temperature regions while the modified spin wave theory is good for low temperatures. Moreover, the convergence regions of the cumulant expansion and the modified spin wave theory overlap each other which propose these two as a set of complement methods to get the thermodynamic properties of spin models.

1/T1 nuclearrelaxation time of κ-(BEDT–TTF)2Cu[N(CN)2]Cl : effects of magnetic frustration

We study the role played by the magnetic frustration in the antiferromagnetic phase of the organicsalt κ-(BEDT–TTF)2Cu[N(CN)2]Cl. Using the spatially anisotropic triangular Heisenberg model we analyseprevious and newly performed NMR experiments. We compute the1/T1 relaxation time by means of the modified spin wave theory. The strong suppression ofthe nuclear relaxation time observed experimentally under varying pressure andmagnetic field is qualitatively well reproduced by the model. Our results suggest theexistence of a close relation between the effects of pressure and magnetic frustration.

Modified Spin-Wave Theory of Nuclear Magnetic Relaxation in One-Dimensional Quantum Ferrimagnets: Three-Magnon versus Raman Processes

Nuclear spin-lattice relaxation in one-dimensional Heisenberg ferrimagnets is studied by means of a modified spin-wave theory. Calculating beyond the first-order mechanism, where a nuclear spin directly interacts with spin waves through the hyperfine coupling, we demonstrate that the exchange-scattering-enhanced three-magnon nuclear relaxation may generally predominate over the Raman one with increasing temperature and decreasing field. Recent proton spin-lattice relaxation-time (T_1_) measurements on the ferrimagnetic chain compound NiCu(C_7_H_6_N_2_O_6_)(H_2_O)_3_2H_2_O suggest that the major contribution to 1/T_1_ be made by the three-magnon scattering.