Critical exponents for two-dimensional Heisenberg ferromagnet with long-range interaction

Summary Using renormalization group technique, the critical exponents are determined for two-dimensional Heisenberg ferromagnet in the presence of a magnetic field. Critical exponents are expressed as a function of potential range σ. For the long-range interaction potential between the spins, the spontaneous magnetization exponent β takes the poorer value of mean-field result. The other exponents agree with the known values of exponents. The susceptibility eigenvalue equation arising from renormalization group is also solved and eigenfunctions are determined.

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Riassunto Usando la tecnica del gruppo di rinormalizzazione si determinano gli esponenti critici per un ferromagnete di Heisenberg bidimensionale in presenza di un campo magnetico. Si esprimono gli esponenti critici in funzione di un intervallo di potenziale σ. Per un potenziale d’interazione a largo raggio tra gli spin, l’esponente di magnetizzazione spontanea β assume il valore più scarso del risultato del campo medio. Gli altri esponenti si accordano con i valori noti degli esponenti. Si risolve anche l’equazione degli autovalori di suscettibilità proveniente dal gruppo di rinormalizzazione e si determinano le autofunzioni.

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Резюме Используя технику грушы перенормировки, определяются критические экспоненты для двумерного ферромагнетика Гайзенберга в присутствии магнитного поля. Критические экспоненты выражаются через радиус действия потенциала. Для длиннодействующго потенциала взаимодействия между спинами зкспонента спонтанного нмагничивания β дает меньшую величину для среднего поля. Другие экспоненты согласуются с известными величинами для экспонент. Решается уравнение для собоственных значений восприимчивости, возникающее из группы перенормировки, и определяются собственные функции.

     

Bond-Alternating Antiferromagnetic S=1/2 Heisenberg Ladder with Ferromagnetic Diagonal Coupling

Using the density matrix renormalization group method, we determine the phase diagram of a frustrated bond-alternating S=1/2 Heisenberg ladder with ferro-antiferromagnetic couplings at zero temperature. With the interactions between spins along the rungs set, we identify three spin-gapped phases （the Haldane phase, the singlet phase and the dimer phase） in the whole parameter range. The analysis of our data shows that two-leg spin bond-alternating ladders have a rich phase diagram if both rung and diagonal couplings are taken into account.     

Elementary spin excitations in a Heisenberg S=1/2 antiferromagnet with Skyrmions

The elementary spin excitations in two-dimensional Heisenberg antiferromagnets with spin S=1/2 in a metastable, spatially inhomogeneous state are investigated. The energy spectrum of the excitations, the local order parameter, and the temperature dependence of the spin correlation length are found. It is shown that the results obtained can be used to explain the experimental data on neutron scattering in La₂CuO₄ at temperatures T>T _N. Fiz. Tverd. Tela (St. Petersburg) 39, 656–659 (April 1997)     

Incommensurate phases in ferromagnetic spin-chains with weak antiferromagnetic interchain interaction

We study planar ferromagnetic spin-chain systems with weak antiferromagnetic inter-chain interaction and dipole-dipole interaction. The ground state depends sensitively on the relative strengths of antiferromagnetic exchange and dipole energies κ = J′a ² c/(g _L μ _B )². For increasing values of κ, the ground state changes from a ferromagnetic via a collinear antiferromagnetic and an incommensurate phase to a 120° structure for very large antiferromagnetic energy. Investigation of the magnetic phase diagram of the collinear phase, as realized in CsNiF₃, shows that the structure of the spin order depends sensitivly on the direction of the magnetic field in the hexagonal plane. For certain angular domains of the field incommensurate phases appear which are seperated by commensurate phases. When rotating the field, the wave vector characterizing the structure changes continously in the incommensurate phase, whereas in the commensurate phase the wave vector is locked to a fixed value describing a two-sublattice structure. This is a result of the competition between the exchange and the dipole-dipole interaction.     

String order and degenerate entanglement spectrum of S = 1 / 2 and S = 1 Heisenberg bond-alternating chains

Generalized string orders and entanglement spectrum of S = 1/2 and S = 1 Heisenberg bond-alternating chains have been investigated by the infinite time-evolving block decimation (iTEBD) method. Generalized string order parameters with appropriate θ are capable of distinguishing all the topological phases. Central charges c ? 1 and critical exponents β ?1/12 indicate all the topological QPTs belong to the Gaussian universality class. Interestingly, odd- and even-fold degeneracies of the entanglement spectrum are observed. Even-fold (doubly) degenerate entanglement spectra and the typical two-fold degenerate lowest-lying level are found to exist in both the spin-1/2 dimer and the S = 1 Haldane phases. However, odd-fold degenerate entanglement spectra with three-fold degenerate lowest-lying level are observed in both the S = 1 dimer and the S = 2 Haldane phase. The degeneracy of the lowest-lying entanglement spectrum level, which can be understood by entanglement spectra in the dimer limit (J ₁ = 0), is adopted to estimate the lowest boundary of the bipartite entanglement. The entanglement spectrum and the generalized string orders are valuable for uncovering the underlying features of these symmetry-protect topological (SPT) states. Similar entanglement spectrum shows that the S = 1 (S = 2) Haldane phase is essentially the same as the S = 1/2 (S = 1) dimer phase.     

Quantum Monte Carlo investigation of the 2D Heisenberg model with S=1/2

The two-dimensional (2D) Heisenberg model with anisotropic exchange (Δ = 1−J _x /J _z ) and S=1/2 is investigated by the quantum Monte Carlo method. The energy, susceptibility, specific heat, spin-spin correlation functions, and correlation radius are calculated. The sublattice magnetization (σ) and the Néel temperature of the anisotropic antiferromagnet are logarithmic functions of the exchange anisotropy: 1/σ+1+0.13(1)ln(1/Δ). Crossover of the static magnetic structural factor as a function of temperature from power-law to exponential occurs for T _c /J≈0.4. The correlation radius can be approximated by 1/ξ=2.05T ^1.0(6)/exp(1.0(4)/T). For La₂CuO₄ the sublattice magnetization is calculated as σ=0.45, the exchange is J=(1125–1305) K; for Er₂CuO₄ J∼625 K and the exchange anisotropy Δ∼0.003. The temperature dependence of the static structural magnetic factor and the correlation radius above the Néel temperature in these compounds can be explained by the formation of topological excitations (spinons). Fiz. Tverd. Tela (St. Petersburg) 41, 116–121 (January 1999)     

Ising phases of Heisenberg ladders in a magnetic field

We show that Dzyaloshinskii-Moriya (DM) interactions can substantially modify the phase diagram of spin-1/2 Heisenberg ladders in a magnetic field provided they compete with exchange. For nonfrustrated ladders, they induce a local magnetization along the DM vector that turns the gapless intermediate phase into an Ising phase with broken translational symmetry, while for frustrated ladders, they extend the Ising order of the half-integer plateau to the surrounding gapless phases of the purely Heisenberg case. Implications for experimental ladder and dimer systems are discussed.     

Spin-exchange dynamical structure factor of the S=1/2 Heisenberg chain

We determine the spin-exchange dynamical structure factor of the Heisenberg spin chain, as is measured by indirect resonant inelastic x-ray scattering (RIXS). We find that two-spin RIXS excitations nearly entirely fractionalize into two-spinon states. These share the same continuum lower bound as single-spin neutron scattering excitations, even if the relevant final states belong to orthogonal symmetry sectors. The RIXS spectral weight is mainly carried by higher-energy excitations, and is beyond the reach of the low-energy effective theories of Luttinger liquid type.     

0- and 2/3-magnetization plateaus in three-leg antiferromagnetic Heisenberg spin-1/2 ladders with leg-dimerization

Magnetic properties of three-leg antiferromagnetic Heisenberg spin-1/2 ladders with different dimerization patterns have been studied using the bond mean-field theory. Our results show that rung-columnar ladders are thermodynamically stable states for large rung-to-leg coupling ratios. Magnetization curves of leg-columnar and leg-staggered ladders always exhibit 0- and 2/3-magnetization plateaus, which do not appear in rung-columnar and rung-staggered ladders. In leg-dimerized ladders, the formation of spin dimers in the three legs results in the appearance of the 0- and 2/3-magnetization plateaus. Spin configuration in the 2/3-magnetization plateau can be understood from the mean-field bond parameters.     

Investigation of the magnetic properties of chains with alternating ferro-and antiferromagnetic exchange interactions in the Heisenberg model with spin S=1/2

The quantum Monte Carlo method is used to calculate the susceptibility and pairwise spin-spin correlation functions of chains with alternating ferro (K)-and antiferromagnetic (J)-exchange interactions within the Heisenberg model with spin S=1/2. From the susceptibility, the energy gap between the ground state and excited triplet states is determined or arbitrary ratios K/J. The value of the gap coincides with the Haldane gap for spin S=1 when K/J>1.25. Fiz. Tverd. Tela (St. Petersburg) 41, 1650–1651 (September 1999)     

Longitudinal Susceptibility of S = 1/2 Low-Dimensional Heisenberg Ferromagnet in a Magnetic Field

Longitudinal susceptibility of the spin-1/2 low-dimensional Heisenberg ferromagnet in a magnetic field, is studied by the Green's function method within the random phase approximation. The static and dynamic longitudinal susceptibilities are calculated in the low- and high-field regions. Power laws for the position and height of the static susceptibility maximum are shown not to support the predictions of Landau theory.     

Thermodynamic properties of the spin-1/2 ferromagnetic Heisenberg chain with long-range interactions

The one-dimensional spin-1/2 XYZ ferromagnetic model in a transverse field and uniform long-range interactions among the z components of the spins is studied using the mean-field Jordan–Wigner transformation. The thermodynamic quantities results like Helmholtz free energy, the internal energy, the specific heat and the isothermal susceptibility are obtained both analytically and numerically. The phase transition of the system at a finite temperature is also discussed. Our results agree with numerical results of the XYZ spin chain by others.