Static Spin Structure Factor Research Articles

Field induced quantum phase transition in the anisotropic spin ladder

We have studied the quantum phase transition between antiferromagnetic and spin liquid phases for field induced quasi-one dimensional spin ladder model Hamiltonian. Using bond operator formalism, the original spin Hamiltonian is mapped to bosonic one. Green's function approach has been implemented to get the low energy spectrum and the corresponding structure factor. The critical field (Bc) for a fixed coupling exchange between two rungs is found based on the Bose–Einstein condensation of quasi-particles (triplons) which takes place when the spin excitation spectrum vanishes at the antiferromagnetic wave vector. We have investigated the effect of both intersite (δ) and local (Δ) anisotropy on the critical field, critical coupling exchange and transverse static structure factor of the field induced quasi-one dimensional antiferromagnetic anisotropic spin ladder model at zero temperature. We have also studied the divergent behavior of static spin structure factor when magnetic field approaches the critical point.

Ground-state properties of the one-dimensional extended Hubbard model at half filling

The density-matrix renormalization group (DMRG) technique is used to study the ground-state properties of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U ( V) and nearest-neighbor hopping t. We calculate the static spin structure factor to consider the spin degrees of freedom. We notice a striking difference of the static spin structure factor among the spin-density-wave, charge-density-wave (CDW), and bond-order-wave (BOW) phases. Based on the results, we identify the BOW–CDW transition at small (large) U value as continuous (of first order). We also calculate the double occupancy to consider the charge degrees of freedom. For large U, the double occupancy show a discontinuous jump at the BOW–CDW critical point and it implies first-order transition. With decreasing U, the jump becomes smaller and vanishes at the tricritical point U t ≈ 5.961 t . This value is close to our previous estimation U t = 5.89 t obtained with other quantities. Consequently, the results of static spin structure factor and double occupancy support the accuracy of our ground-state phase diagram.

Spirals in the t– J model and structure of the spin-glass state of [formula omitted

Starting from the extended t– J model, we derive an effective model that describes the spin dynamics in the insulating phase of La 2 - x Sr x CuO 4 , x ≲ 0.055 , at low temperature. Using Monte Carlo simulations, we show that the destruction of Néel order is driven by the single-hole localization length. A phase transition at 2% doping is consistent with the value of the localization length known from the variable range hopping conductivity. The static spin structure factor obtained in our calculations is in perfect agreement with neutron scattering data over the whole range of doping. Thus we demonstrate that the ground state of La 2 - x Sr x CuO 4 at 0.02 < x < 0.055 is not a simple spin glass, it is a disordered spin spiral state.

Fulde-Ferrell-Larkin-Ovchinnikov pairing in one-dimensional optical lattices

Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method, we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long-range order and oscillations at the wave number expected from the FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for a small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long-range order into long-range order by coupling many identical 1D systems, such as in quasi-1D optical lattices.

Spin structure factors and valence-bond-solid states of the trimerized Heisenberg chains in a magnetic field

By means of the density matrix renormalization group (DMRG) method, the static spin structure factors and the magnetization plateaus of the trimerized Heisenberg ferromagnet–ferromagnet–antiferromagnet and antiferromagnet–antiferromagnet–ferromagnet spin chains in the presence of a magnetic field are elaborately studied. It is found that in the plateau states, the static structure factor with three peaks does not vary with the external magnetic field as well as the exchange couplings; the spin correlation function behaves as a perfect sequence and has a simple relation with the magnetization per site. An approximate wave function for the plateau states is proposed, and a picture based on the valence-bond-solid states is presented in order to understand the origin and the total number of the magnetization plateaus, which are shown to be in agreement with the DMRG results.

Kagome antiferromagnet: A Schwinger-boson mean-field theory study

liquid state for spin S = 1/2 and a mixed state with both q = 0 and p 3 × p 3 orders for spin S > 1/2. We emphasize that the mixed state exhibits two sets of peaks in the static spin structure factor. And for the case of spin S = 1/2, the gap value we obtained is consistent with the previous numerical calculations by other means. We also discuss the thermodynamic quantities such as the specific heat and magnetic susceptibility at low temperatures and show that our result is in a good agreement with the Mermin-Wagner theorem.

Chiral plaquette polaron theory of cuprate superconductivity

Ab initio density functional calculations on explicitly doped ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$ find that doping creates localized holes in out-of-plane orbitals. A model for cuprate superconductivity is developed based on the assumption that doping leads to the formation of holes on a four-site Cu plaquette composed of the out-of-plane ${A}_{1}$ orbitals apical $\mathrm{O}\phantom{\rule{0.2em}{0ex}}{p}_{z}$, planar $\mathrm{Cu}\phantom{\rule{0.2em}{0ex}}{d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$, and planar $\mathrm{O}\phantom{\rule{0.2em}{0ex}}{p}_{\ensuremath{\sigma}}$. This is in contrast to the assumption of hole doping into planar $\mathrm{Cu}\phantom{\rule{0.2em}{0ex}}{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and $\mathrm{O}\phantom{\rule{0.2em}{0ex}}{p}_{\ensuremath{\sigma}}$ orbitals as in the $t\text{\ensuremath{-}}J$ model. Allowing these holes to interact with the ${d}^{9}$ spin background leads to chiral polarons with either a clockwise or anticlockwise charge current. When the polaron plaquettes percolate through the crystal at $x\ensuremath{\approx}0.05$ for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$, a $\mathrm{Cu}\phantom{\rule{0.2em}{0ex}}{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and planar $\mathrm{O}\phantom{\rule{0.2em}{0ex}}{p}_{\ensuremath{\sigma}}$ band is formed. The computed percolation doping of $x\ensuremath{\approx}0.05$ equals the observed transition to the ``metallic'' and superconducting phase for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$. Spin exchange Coulomb repulsion with chiral polarons leads to $d$-wave superconducting pairing. The equivalent of the Debye energy in phonon superconductivity is the maximum energy separation between a chiral polaron and its time-reversed partner. This energy separation is on the order of the antiferromagnetic spin coupling energy, ${J}_{dd}\ensuremath{\sim}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, suggesting a higher critical temperature. An additive skew-scattering contribution to the Hall effect is induced by chiral polarons and leads to a temperature dependent Hall effect that fits the measured values for ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$. The integrated imaginary susceptibility, observed by neutron spin scattering, satisfies $\ensuremath{\omega}∕T$ scaling due to chirality and spin-flip scattering of polarons along with a uniform distribution of polaron energy splittings. The derived functional form is compatible with experiments. The static spin structure factor for chiral spin coupling of the polarons to the undoped antiferromagnetic $\mathrm{Cu}\phantom{\rule{0.2em}{0ex}}{d}^{9}$ spins is computed for classical spins on large two-dimensional lattices and is found to be incommensurate with a separation distance from $(\ensuremath{\pi}∕a,\ensuremath{\pi}∕a)$ given by $\ensuremath{\delta}Q\ensuremath{\approx}(2\ensuremath{\pi}∕a)x$, where $x$ is the doping. When the perturbed ${x}^{2}\ensuremath{-}{y}^{2}$ band energy in mean field is included, incommensurability along the Cu-O bond direction is favored. A resistivity $\ensuremath{\sim}{T}^{\ensuremath{\mu}+1}$ arises when the polaron energy separation density is of the form $\ensuremath{\sim}{\ensuremath{\Delta}}^{\ensuremath{\mu}}$ due to Coulomb scattering of the ${x}^{2}\ensuremath{-}{y}^{2}$ band with polarons. A uniform density leads to linear resistivity. The coupling of the ${x}^{2}\ensuremath{-}{y}^{2}$ band to the undoped $\mathrm{Cu}\phantom{\rule{0.2em}{0ex}}{d}^{9}$ spins leads to the angle-resolved photoemission pseudogap and its qualitative doping and temperature dependence. The chiral plaquette polaron leads to an explanation of the evolution of the bilayer splitting in Bi-2212.

Structure of the Spin-Glass State ofLa2−xSrxCuO4: The Spiral Theory

Starting from the t-J model, we derive an effective field theory describing the spin dynamics in the insulating phase of La_{2-x}Sr_xCuO_4, x < 0.055, at low temperature. Using Monte Carlo simulations, we show that the destruction of Neel order is driven by the single-hole localization length kappa. A phase transition at 2% doping is consistent with the value of kappa known from the variable range hopping conductivity. The static spin structure factor obtained in our calculations is in perfect agreement with neutron scattering data over the whole range of doping. We also demonstrate that topological defects (spin vortex-antivortex pairs) are an intrinsic property of the spin-glass ground state.

Quantum fluctuations and excitations in antiferromagnetic quasicrystals

We study the effects of quantum fluctuations and the excitation spectrum for the antiferromagnetic Heisenberg model on a two-dimensional quasicrystal, by numerically solving linear spin-wave theory on finite approximants of the octagonal tiling. Previous quantum Monte Carlo results for the distribution of local staggered magnetic moments and the static spin structure factor are reproduced well within this approximate scheme. Furthermore, the magnetic excitation spectrum consists of magnon-like low-energy modes, as well as dispersionless high-energy states of multifractal nature. The dynamical spin structure factor, accessible to inelastic neutron scattering, exhibits linear-soft modes at low energies, self-similar structures with bifurcations emerging at intermediate energies, and flat bands in high-energy regions. We find that the distribution of local staggered moments stemming from the inhomogeneity of the quasiperiodic structure leads to a characteristic energy spread in the local dynamical spin susceptibility, implying distinct nuclear magnetic resonance spectra, specific for different local environments.

Magnetic Correlations in CuGeO 3

The static spin structure factor S(Q) of CuGeO3 was determined above its spin-Peierls transition temperature by inelastic neutron scattering. At 20 K, S(Q) has a Lorentzian line shape centered at the antiferromagnetic (AF) zone center. With increasing temperature, however, it splits into two peaks with their centers at incommensurate wave vectors at higher temperatures (70 and 120 K). The observed results are consistent with the prediction by recent numerical studies on the S = 1/2 Heisenberg AF chain with competing spin interactions [I. Harada and Y. Aoyama, (1999) “Static spin structure factor of CuGeO3 above spin-Peierls transition temperature”, J. Phys. Chem. Solids 60, 1105; I. Harada, Y. Nishiyama, Y. Aoyama and S. Mori, (2000) “Spin correlation in the one-dimensional Heisenberg antiferromagnet with competing interactions”, J. Phys. Soc. Jpn. 69, (Suppl. A), 339].

Finite-temperature structure factor in the Haldane–Shastry spin chain

The Haldane-Shastry spin chain can be mapped to the infinite coupling limit of the SU(2) spin Calogero-Sutherland model. We use the $\mathfrak{gl}_2$ Jack polynomials' technology to compute the form factors of the spin operator on the multi-spinon spectrum. The spin structure factor is obtained through a form factor expansion. The expansion is proven to converge in the small momentum limit. Numerics based on two- and four-spinons contributions give an approximate result for the infinite temperature static and dynamic spin structure factor.

Quantum antiferromagnets on pyrochlore lattice

We have investigated on the low-temperature properties of the S= 1 2 quantum aniferromagnetic spin systems on the pyrochlore lattice. The static-spin structure factors have been calculated , using the bond-operator method, in order to clarify the physical picture of the disordered ground state of this highly frustrated system. The result shows that the wave vector dependence on [0 0 h]–[h h 0] plane of the reciprocal space obtained by Canals and Lacroix ( Phys. Rev. Lett. 80 (1998) 2933), can be qualitatively understood in terms of the valence bond solid picture.

ChemInform Abstract: Finite-Temperature Properties of Doped Antiferromagnets

We review recent results for the properties of doped antiferromagnets, obtained by the numerical analysis of the planar t-J model using the novel finite-temperature Lanczos method for small correlated systems. First we briefly summarize our present understanding of anomalous normal-state properties of cuprates, and present the electronic phase diagram, phenomenological scenarios and models proposed in this connection. The numerical method is then described in more detail. The following sections are devoted to various static and dynamical properties of the t-J model. Among the thermodynamic properties the chemical potential, entropy and the specific heat are evaluated. Discussing electrical properties the emphasis is on the planar optical conductivity and the d.c. resistivity. Magnetic properties involve the static and dynamical spin structure factor, as measured via the susceptibility measurements, the NMR relaxation and the neutron scattering, as well as the orbital current contribution. The analysis of ...

Finite-temperature properties of doped antiferromagnets

We review recent results for the properties of doped antiferromagnets, obtained by the numerical analysis of the planar t-J model using the novel finite-temperature Lanczos method for small correlated systems. First we briefly summarize our present understanding of anomalous normal-state properties of cuprates, and present the electronic phase diagram, phenomenological scenarios and models proposed in this connection. The numerical method is then described in more detail. The following sections are devoted to various static and dynamical properties of the t-J model. Among the thermodynamic properties the chemical potential, entropy and the specific heat are evaluated. Discussing electrical properties the emphasis is on the planar optical conductivity and the d.c. resistivity. Magnetic properties involve the static and dynamical spin structure factor, as measured via the susceptibility measurements, the NMR relaxation and the neutron scattering, as well as the orbital current contribution. The analysis of electron spectral functions, studied by photoemission experiments, and their relation to the c-axis conductivity, follows. Finally we discuss density fluctuations, the electronic Raman scattering and the thermoelectric power. Whenever feasible a comparison with experimental data is performed. A general conclusion is that the t-J model captures well the main features of anomalous normal-state properties of cuprates, for a number of quantities the agreement is even a quantitative one. It is shown that several dynamical quantities exhibit at intermediate doping a novel universal behaviour consistent with a marginal Fermi-liquid concept, which seems to emerge from a large degeneracy of states and a frustration induced by doping the antiferro magnet.

Static spin structure factor of CuGeO 3 above spin-Peierls transition temperature

We study, by means of the quantum transfer matrix method, the finite-temperature behavior of the S=1/2 antiferromagnetic chain with nearest neighbor and competing next nearest neighbor interactions, which is a model for the spin-Peierls material, CuGeO 3. In particular, the static spin structure factor is found to display an interesting phenomenon as a consequence of the competition: a characteristic wave number for the maximum value of the structure factor takes a commensurate or an incommensurate value, depending on temperature. The boundary, called a Lifshitz temperature, can be found in this material. We discuss such behavior in connection with the experimental result of the neutron scattering in CuGeO 3 above the spin-Peierls transition temperature.

Numerical study of the two-dimensional Heisenberg model using a Green function Monte Carlo technique with a fixed number of walkers

We describe in detail a simple and efficient Green function Monte Carlo technique for computing both the ground state energy and the ground state properties by the ``forward walking'' scheme. The simplicity of our reconfiguration process, used to maintain the walker population constant, allows us to control any source of systematic error in a rigorous and systematic way. We apply this method to the Heisenberg model and obtain accurate and reliable estimates of the ground state energy, the order parameter, and the static spin structure factor $S(q)$ for several momenta. For the latter quantity we also find very good agreement with available experimental data on the ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ antiferromagnet.

Dynamical properties of the spin-Peierls compoundα′−NaV2O5

Dynamical properties of the novel inorganic spin-Peierls compound \alpha'--NaV2O5 are investigated using a one-dimensional dimerized Heisenberg model. By exact diagonalizations of chains with up to 28 sites, supplemented by a finite-size scaling analysis, the dimerization parameter \delta is determined by requiring that the model reproduces the experimentally observed spin gap \Delta. The dynamical and static spin structure factors are calculated. As for CuGeO3, the existence of a low energy magnon branch separated from the continuum is predicted. The present calculations also suggest that a large magnetic Raman scattering intensity should appear above an energy threshold of 1.9 \Delta. The predicted photoemission spectrum is qualitatively similar to results for an undimerized chain due to the presence of sizable short-range antiferromagnetic correlations.

Two-spinon dynamic structure factor of the one-dimensional s= Heisenberg antiferromagnet

The exact expression derived by Bougourzi, Couture, and Kacir for the 2-spinon contribution to the dynamic spin structure factor $S_{zz}(q,\omega)$ of he one-dimensional $S$=1/2 Heisenberg antiferromagnet at $T=0$ is evaluated for direct comparison with finite-chain transition rates ($N\leq 28$) and an approximate analytical result previously inferred from finite-$N$ data, sum rules, and Bethe-ansatz calculations. The 2-spinon excitations account for 72.89% of the total intensity in $S_{zz}(q,\omega)$. The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the 2-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and $q$-dependent susceptibility are determined via sum rules.

Uncompensation Effect in a One-Dimensional Alternating-Spin Ising Ferrimagnet with Competing Interactions

The characteristic short-range orders (SROs) in a one-dimensional Ising ferrimagnet, which is composed of alternating spins with different spin quantum numbers, Lande g -factors, and next-nearest-neighbor interactions, are investigated by the numerically exact calculation of a nonsymmetric transfer matrix. Due to the uncompensating moments, some SROs in the system show very different characteristics from those in the uniform-spin ANNNI chain; (i) the peculiar two-peaked structure of the static spin structure factor S ( q ), indicating not two different SROs but the same SRO, and (ii) an unusual thermal recovery of the ferrimagnetic SRO, carrying three disorder points, under a non-zero external field. Decaying features of the characteristic SROs and the magnetic behavior of the system with variation of external field are also discussed.

Effect of a Symmetry-Breaking Field on the Ground State of the Spin-1/2 Antiferromagnetic Linear Chain

We investigate the ground-state property of the one-dimensional spin-1/2 antiferromagnetic X X Z chain in a symmetry-breaking field, by means of numerical diagonalization method for finite-size spin systems combined with the phenomenological renormalization group method. It is found that, with increasing field, there occurs the ground-state phase transition from an ordered phase to a disordered phase, whose critical property belongs to the universality class of the transverse Ising model. The ground-state phase diagram is determined in two parameter regions; (i) an Ising-like region and (ii) an X Y -like region. Our inspection of the field dependence of the energy gap and the static spin structure factors reveals that the ordered phase in both regions exhibits the characteristics of Neel order. Quantum nature of the ground state is also briefly discussed.