Physical spin configurations corresponding to topological excitations, expected to be present in the XY limit of a quantum spin 1/2 Heisenberg anti-ferromagnet, are probed on a two dimensional square lattice . Quantum vortices (anti-vortices) are constructed in terms of coherent staggered spin field components, as limiting case of meronic (anti-meronic) configurations . The crucial role of the associated Wess-Zumino-like (WZ-like) term is highlighted in our procedure . The time evolution equation of coherent spin fields used in this analysis is obtained by applying variational principle on the quantum Euclidean action corresponding to the Heisenberg anti-ferromagnet on lattice . It is shown that the WZ-like term can distinguish between vortices and anti-vortices only in a charge sector with odd topological charges. Our formalism is distinctly different from the conventional approach for the construction of quantum vortices (anti-vortices) .
The spin-1/2 Ising-Heisenberg model on martini and martini-diced lattice is exactly solved using a star-triangle transformation, which affords an exact mapping correspondence to an effective spin-1/2 Ising model on a triangular lattice. The ground-state phase diagram of both investigated quantum spin models display two spontaneously ordered ferromagnetic phases and one macroscopically degenerate disordered phase. In contrast to a classical ferromagnetic phase where the spontaneous magnetization of the Ising as well as Heisenberg spins acquire fully saturated values the spontaneous magnetizatio…
A bipartite entanglement between two nearest-neighbor Heisenberg spins of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is quantified using a concurrence. It is shown that the concurrence equals zero in a classical ferromagnetic and a quantum disordered phase, while it becomes sizable though unsaturated in a quantum ferromagnetic phase. A thermally-assisted reentrance of the concurrence is found above a classical ferromagnetic phase, whereas a quantum ferromagnetic phase displays a striking cusp of the concurrence at a critical temperature.
The spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with ferromagnetic next-nearest-neighbour (NNN) interaction is investigated. The ground state is the Haldane phase for weak NNN interaction, and is the ferromagnetic phase for weak antiferromagnetic interaction. We find a series of topologically distinct spin-gap phases with various magnitudes of edge spins for strong NNN interaction. The phase boundaries between these phases are determined on the basis of the DMRG calculation with additional spins that compensate the edge spins. It is found that each of the exact soluti…
Using a functional renormalization group approach we show that at low temperatures and in a certain range of magnetic fields the longitudinal dynamic structure factor of quantum Heisenberg ferromagnets in dimensions $D\leq 2$ exhibits a well-defined quasi-particle peak with linear dispersion that we identify as zero-magnon sound. In $D>2$ the larger phase space available for the decay into transverse spin waves leads only to a broad hump centered at zero frequency whose width scales linearly in momentum.
The topological classification of a series of frustration-induced spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with next-nearest-neighbour interaction reported in J. Phys. Soc. Jpn. 82, 064703 (2013) is confirmed using two kinds of entanglement spectra defined by different divisions of the whole chain. For the numerical calculation, the iDMRG method is used. The results are consistent with the valence bond solid picture proposed in the previous paper.
The ground state phase diagram of the spin-1/2 Heisenberg frustrated $Δ$-chain with a ferromagnetic main chain is investigated. In addition to the ferromagnetic phase, various nonmagnetic ground states are found. If the ferromagnetic coupling between apical spins and the main chain is strong, this model is approximated by a spin-1 bilinear-biquadratic chain and the spin quadrupolar phase with spin-2 gapless excitation is realized in addition to the Haldane and ferromagnetic phases. In the regime where the coupling between the apical spins and the main chain is weak, the numerical results which…
The spin-1/2 Heisenberg model is formulated in terms of a mean-field approximation (MFA) by using the matrix forms of spin operators $\hat{S}_x,\hat{S}_y$ and $\hat{S}_z$ in three-dimensions. The considered Hamiltonian consists of bilinear exchange interaction parameters $(J_x,J_y,J_z)$, Dzyaloshinskii-Moriya interactions $(Δ_x,Δ_y,Δ_z)$ and external magnetic field components $(H_x,H_y,H_z)$. The magnetization and its components are obtained in the MFA with the general anisotropic case with $J_x\neq J_y \neq J_z$ for various values of coordination numbers $q$. Then, the thermal variations of m…
Effect of biquadratic exchange on phase transitions of a planar classical Heisenberg (or XY) ferromagnet on a stacked triangular lattice is investigated by Standard Monte Carlo and Histogram Monte Carlo simulations in the region of a bilinear to biquadratic exchange interaction ratio $J_{1}/J_{2} \leq 1$. The biquadratic exchange is found to cause separate second-order phase transitions in a strong biquadratic exchange limit, followed by simultaneous dipole and quadrupole ordering, which is of first order for an intermediate range of the exchange ratio and changes to a second-order one again a…
We study Heisenberg antiferromagnets on a diamond-like decorated square lattice perturbed by further neighbor couplings. The second-order effective Hamiltonian is calculated and the resultant Hamiltonian is found to be a square-lattice quantum-dimer model with a finite hopping amplitude and no repulsion, which suggests the stabilization of the plaquette phase. Our recipe for constructing quantum-dimer models can be adopted for other lattices and provides a route for the experimental realization of quantum-dimer models.
We present the phase diagram of the frustrated ferromagnetic S=1/2 Heisenberg J_1-J_2 chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states towards spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in …
We consider Gaussian fluctuations about domain walls embedded in one- or two-dimensional spin lattices. Analytic expressions for the free energy of one domain wall are obtained. From these, the temperature dependence of experimentally relevant spatial scales -- i.e., the correlation length for spin chains and the size of magnetic domains for thin films magnetized out of plane -- are deduced. Stability of chiral order inside domain walls against thermal fluctuations is also discussed.
Ferromagnetic-paramagnetic phase transitions in classical and quantum thin films have been studied up to 50 mono-layers using effective field theory with two-site cluster approximation. Variation of the Curie temperature as a function of film thickness has been examined. The relative shift of the Curie temperature from the corresponding bulk value has been investigated in terms of the shift exponent $λ$. We have found that shift exponent $λ$ clearly depends on the strength of the ferromagnetic exchange coupling of the surface. Moreover, we have not observed any significant difference between c…
We study the universal far from equilibrium dynamics of magnons in Heisenberg ferromagnets. We show that such systems exhibit universal scaling in momentum and time of the quasiparticle distribution function, with the universal exponents distinct from those recently observed in Bose-Einstein condensates. This new universality class originates from the SU(2) symmetry of the Hamiltonian, which leads to a strong momentum-dependent magnon-magnon scattering amplitude. We compute the universal exponents using the Boltzmann kinetic equation and incoherent initial conditions that can be realized with …
The Quantum Heisenberg Ferromagnet can be naturally reformulated in terms of interacting bosons (called spin waves or magnons) as an expansion in the inverse spin size. We calculate the first order interaction correction to the free energy, as an upper bound in the limit where the spin size $S \to \infty$ and $βS$ is fixed ($β$ being the inverse temperature). Our result is valid in two and three spatial dimensions. We extrapolate our result to compare with Dyson's low-temperature expansion. While our first-order correction has the expected temperature dependance, in higher orders of the pertur…
The one dimensional (1D) spin-1/2 Heisenberg-Ising model, a prototype quantum many-body system, has been intensively studied for many years. In this review, after a short introduction on some basic concepts of group theory for the octahedral group, a detailed pedagogical framework is laid down to derive the low-energy effective Hamiltonian for the Co-based materials. The 1D spin-1/2 Heisenberg-Ising model is obtained when applying the analysis to quasi-1D antiferromagnetic materials $\rm BaCo_2V_2O_8$ and $\rm SrCo_2V_2O_8$. After the preparation, we review the theoretical progresses of a vari…
The thermodynamics of a site-diluted ferromagnetic Heisenberg model for spin $S=1/2$ with interaction anisotropy in spin space is investigated. The study is aimed at presenting the magnetocaloric properties of such a model, including the entropy and temperature changes in magnetization/demagnetization processes, generalized Grüneisen ratio as well as the quantities characterizing the efficiency of magnetic cooling cycles. The results are obtained using Pair Approximation (PA) method and extensively compared with the Molecular Field Approximation (MFA) calculations. The importance of interactio…
A series of symmetry-protected topological(SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In the case one of the next-nearest-neighbor interaction vanishes, the model reduces to the $Δ$-chain in which a series of spin-gap phases are found in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and triv…
We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in the absence of an external field. Spin wave theory suggests that in a suitable temperature regime the system behaves effectively as a system of non-interacting bosons (magnons). We prove this fact at the level of the specific free energy: if $ S \to \infty $ and the inverse temperature $ β\to 0 $ in such a way that $ βS $ stays constant, we rigorously show that the free energy per unit volume converges to the one suggested by spin wave theory. The proof is based on the localization of the system in small boxes and on…
A study of the d-dimensional classical Heisenberg ferromagnetic model in the presence of a magnetic field is performed within the two-time Green function's framework in classical statistical physics. We extend the well known quantum Callen method to derive analytically a new formula for magnetization. Although this formula is valid for any dimensionality, we focus on one- and three- dimensional models and compare the predictions with those arising from a different expression suggested many years ago in the context of the classical spectral density method. Both frameworks give results in good a…
We investigate the ground-state magnetic order of the spin-1/2 J1-J2 Heisenberg model on the square lattice with ferromagnetic nearest-neighbor exchange J1<0 and frustrating antiferromagnetic next-nearest neighbor exchange J2>0. We use the coupled-cluster method to high orders of approximation and Lanczos exact diagonalization of finite lattices of up to N=40 sites in order to calculate the ground-state energy, the spin-spin correlation functions, and the magnetic order parameter. We find that the transition point at which the ferromagnetic ground state disappears is given by J2^{c1}=0.393|J1|…
The Pair Approximation method has been formulated for the isotropic ferromagnetic Heisenberg model with spin $S=1$. The exchange interactions of arbitrary range have been taken into account. The single-ion anisotropy has been considered as well as the external magnetic field. Within the method, the Gibbs free-energy has been derived, from which all thermodynamic properties can be self-consistently obtained. In order to illustrate the developed formalism, the numerical calculations have been performed for CrIAs planar magnetic semiconductor, a hypothetical material whose existence has been rece…
Using the spin-rotation-invariant Green's function method we calculate the thermodynamic quantities (correlation functions <S_0 S_R>, uniform static spin susceptibility χ, correlation length ξ, and specific heat C_V) of the two-dimensional spin-1/2 J1-J2 Heisenberg ferromagnet for J2 < J2^c \approx 0.44|J1|, where J2^c is the critical frustrating antiferromagnetic next-nearest neighbor coupling at which the ferromagnetic ground state gives way for a ground-state phase with zero magnetization. Examining the low-temperature behavior of χand ξ, in the limit T \to 0 both quantities diverge exponen…
The Monte Carlo method is a powerful technique for computing thermodynamic magnetic states of otherwise unsolvable spin Hamiltonians, but the method becomes computationally prohibitive with increasing number of spins and the simulation of real materials and nanostructures is cumbersome. This paper presents the acceleration of Monte Carlo simulations of the three-dimensional anisotropic Heisenberg model on Graphics-Processing Units (GPU). The GPU implementation of the method presented here provides an acceleration of two orders of magnitude over conventional implementations and enables the simu…
Today, further downscaling of mobile electronic devices poses serious problems, such as energy consumption and local heat dissipation. In this context, spin wave majority gates made of very thin ferromagnetic films may offer a viable alternative. However, similar downscaling of magnetic thin films eventually enforces the latter to operate as quasi-two dimensional magnets, the magnetic properties of which are not yet fully understood, especially those related to anisotropies and external magnetic fields in arbitrary directions. To this end, we have investigated the behaviour of an easy-plane an…
We consider the quantum ferromagnetic Heisenberg model in three dimensions, for all spins $S\geq 1/2$. We rigorously prove the validity of the spin-wave approximation for the excitation spectrum, at the level of the first non-trivial contribution to the free energy at low temperatures. Our proof comes with explicit, constructive upper and lower bounds on the error term. It uses in an essential way the bosonic formulation of the model in terms of the Holstein-Primakoff representation. In this language, the model describes interacting bosons with a hard-core on-site repulsion and a nearest-neigh…
