On the spectral function of a hole in a one-dimensional quantum antiferromagnet

We discuss the spectral function of a single hole moving in a one-dimensional quantum antiferromagnet. The latter is described by an anisotropic version of thet-J model, wheret is the hopping matrix element. We introduce two independent coupling parametersJ andJ for the Ising and the transverse part of the Heisenberg exchange. Strong electronic correlations which are incorporated in the model prevent the use of usual diagrammatic techniques for dynamic Green functions based on Wick's theorem. For that reason a new projection technique for general correlation functions in terms of cumulants is used. We consider the case of max. For the case of small transverse coupling relative to the Ising part, we give exact expressions for the one hole correlation function. In the limit of vanishing spin fluctuations our result reduces to earlier calculations of the motion of a hole in a one-dimensional Néel state. However, the inclusion of the spin fluctuations leads to drastic modifications of the spectral function.     

Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets

The methods of Dyson, Lieb, and Simon are extended to prove the existence of Néel order in the ground state of the 3D spin-1/2 Heisenberg antiferromagnet on the cubic lattice. We also consider the spin-1/2 antiferromagnet on the cubic lattice with the coupling in one of the three lattice directions taken to ber times its value in the other two lattice directions. We prove the existence of Néel order for 0.16r1. For the 2D spin-1/2 model we give a series of inequalities which involve the two-point function only at short distances and each of which would by itself imply Néel order.     

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

Néel order in the ground state of spin-1/2 Heisenberg antiferromagnetic multilayer systems

We show existence of Néel order for the ground state of a system withM two-dimensional layers with spin 1/2 and Heisenberg antiferromagnetic coupling, providedM8. The method uses the infrared bounds for the ground state combined with ideas introduced by Kennedy, Lieb, and Shastry.     

Zero Temperature Phases of the Frustrated <Emphasis Type="Italic">J</Emphasis><Subscript>1</Subscript>–<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> Antiferromagnetic Spin-1/2 Heisenberg Model on a Simple Cubic Lattice

At zero temperature magnetic phases of the quantum spin-1/2 Heisenberg antiferromagnet on a simple cubic lattice with competing first and second neighbor exchanges (J ₁ and J ₂) is investigated using the non-linear spin wave theory. We find existence of two phases: a two sublattice Néel phase for small J ₂ (AF), and a collinear antiferromagnetic phase at large J ₂ (CAF). We obtain the sublattice magnetizations and ground state energies for the two phases and find that there exists a first order phase transition from the AF-phase to the CAF-phase at the critical transition point, p _c =0.56 or J ₂/J ₁=0.28. We also show that the quartic 1/S corrections due spin-wave interactions enhance the sublattice magnetization in both the phases which causes the intermediate paramagnetic phase predicted from linear spin wave theory to disappear.     

Spin dynamics and spin correlations in the spinS=1 two-dimensional square-lattice Heisenberg antiferromagnet La2NiO4

The static and dynamic spin fluctuations in the spinS=1, two-dimensional (2D) square-lattice antiferromagnet La₂NiO₄ have been studied over a wide temperature range using neutron scattering techniques. The spin correlations in La₂NiO₄ exhibit a crossover from two- to three-dimensional (3D) behavior as the Néel temperature is approached from above. Critical slowing down of the low-energy spin fluctuations is also observed just aboveT _N . The correlation length, (T), and the static structure factor,S(0), have been measured and are compared with recent theoretical calculations for the quantum 2D Heisenberg antiferromagnet using microscopic parameters determined from previous spin-wave measurements. Good agreement for (T) is found with the exact low-temperature result of Hasenfratz and Niedermeyer provided that 2 p _s is renormalized by 20% from the spin-wave value.     

Broken symmetry in antiferromagnets

We discuss limitations of the conventional ‘broken symmetry’ picture of the Heisenberg antiferromagnet. The exact results on the ground state of the linear chain and of the three-dimensional Hamiltonian do not show a ‘degeneracy of the vacuum’. With the help of a solvable model it is shown that the correlations in the ground state may have the Néel character, as revealed by the neutron experiments, even though the ground state is quite different from the Néel states. There is no Goldstone mode in the linear chain. The spin of the antiferromagnetic spin wave is 1/2. But the physical states have a doublet of the spin waves which could be regarded as degenerate states of spin 1 and spin 0. The fermionic character is suppressed and the bosonic character revealed, as in the decolouring phenomena in quantum field theory. It is plausible that in the three-dimensional case also there is no Goldstone mode.     

Spin-wave spectrum of a two-dimensional itinerant electron system: Analytic results for the incommensurate spiral phase in the strong-coupling limit

We study the zero-temperature spin fluctuations of a two-dimensional itinerant-electron system with an incommensurate magnetic ground state described by a single-band Hubbard Hamiltonian. We introduce the (broken-symmetry) magnetic phase at the mean-field (Hartree-Fock) level through a spiral spin configuration with characteristic wave vector Q different in general from the antiferromagnetic wave vector Q _AF, and consider spin fluctuations over and above it within the electronic random-phase (RPA) approximation. We obtain a closed system of equations for the generalized wave vector and frequency dependent susceptibilities, which are equivalent to the ones reported recently by Brenig. We obtain, in addition, analytic results for the spin-wave dispersion relation in the strong-coupling limit of the Hubbard Hamiltonian and find that at finite doping the spin-wave dispersion relation has a hybrid form between that associated with the (localized) Heisenberg model and that associated with the (long-range) RKKY exchange interaction. We also find an instability of the spin-wave spectrum in a finite region about the center of the Brillouin zone, which signals a physical instability toward a different spin- or, possibly, charge-ordered phase, as, for example, the stripe structures observed in the high-T _c materials. We expect, however, on physical grounds that for wave vectors external to this region the spin-wave spectrum that we have determined should survive consideration of more sophisticated mean-field solutions. Received 15 September 2000     

Spin-correlations and low lying excited states of the spin-1/2 Heisenberg antiferromagnet on a square lattice

The ground state and the lowest excited states of the spin 1/2-Heisenberg model are investigated by exact diagonalization and variational Monte Carlo techniques. Our trial state represents a generalization of a wave function introduced by Hulthen, Kasteleijn and Marshall. The long range character of the spin-correlation function is in excellent agreement with exact diagonalization and also with recent neutron scattering results for La₂CuO₄. The asymptotic behavior of the spin-correlation function is found to differ from spin-wave theory. From the exact (N<=20 spins) and variational (N<=400) ground state energies we determine as asymptotic values 1.3025 and 1.288, respectively. We calculate the dispersion for the spin-wave excitations and identify an excited triplet which becomes degenerate with the ground state in the thermodynamic limit. This triplet state allows spontaneous symmetry breaking to occur atT=0 K. Quantum fluctuations reduce the sublattice magnetization to an effective value of 0.195 (3) as compared to the Néel-state value of 1/2.     

Antiferromagnetic resonance study of sodalite loaded with sodium by multi-frequency ESR

We have carried out electron spin resonance (ESR) measurements on powder samples of sodalite loaded with Na at several frequencies between 9.7 and 35 GHz and at temperatures between 1.5 and 60 K. The ESR absorption spectrum below a Néel temperature T_N turns into an asymmetric spectrum with a long tail at low fields from a symmetric one above T_N. The line shape of the spectra below T_N is analyzed by a powder pattern simulation of the antiferromagnetic resonance spectra with easy-plane anisotropy. The calculated line shape reproduces the experimental one considerably well by assuming a Gaussian distribution of the zero-field energy gap. We have evaluated a small anisotropy field of about 2×10⁻⁴ T by using the exchange coupling constant calculated from the Weiss and the Néel temperatures. This result indicates that the sodalite loaded with Na is quite an ideal Heisenberg antiferromagnet as expected from the s-electron character of Na clusters and the cubic arrangement of nano-spaces in the sodalite.     

Spin waves in the block checkerboard antiferromagnetic phase

Motivated by the discovery of a new family of 122 iron-based superconductors, we present the theoretical results on the ground state phase diagram, spin wave, and dynamic structure factor obtained from the extended J₁-J₂ Heisenberg model. In the reasonable physical parameter region of K₂Fe₄Se₅, we find that the block checkerboard antiferromagnetic order phase is stable. There are two acoustic spin wave branches and six optical spin wave branches in the block checkerboard antiferromagnetic phase, which have analytic expressions at the high-symmetry points. To further compare the experimental data on neutron scattering, we investigate the saddlepoint structure of the magnetic excitation spectrum and the inelastic neutron scattering pattern based on linear spin wave theory.     

Skyrmion dynamics in single-hole Néel ordered doped two-dimensional antiferromagnets with arbitrary spin

We develop an effective theory to study the skyrmion dynamics in the presence of a hole (removed spins from the lattice) in Néel ordered two-dimensional antiferromagnets with arbitrary spin value S. The general equation of motion for the “mass center” of this structure is obtained. The frequency of small amplitude oscillations of pinned skyrmions around the defect center is calculated. It is proportional to the hole size and inversely proportional to the square of the skyrmion size.     

Microscopic Theory of the Two-Dimensional Quantum Antiferromagnet in a Paramagnetic Phase

We have developed a consistent theory of the Heisenberg quantum antiferromagnet in the disordered phase with a short range antiferromagnetic order on the basis of the path integral for spin coherent states. In the framework of our approach we have obtained the response function for the spin fluctuations for all values of the frequency ω and the wave vector k and have calculated the free energy of the system. We have also reproduced the known results for the spin correlation length in the lowest order in 1/N. We have presented the Lagrangian of the theory in a form which is explicitly invariant under rotations and found natural variables in terms of which one can construct a natural perturbation theory. The short wave spin fluctuations are similar to those in the spin wave theory and they are on the order of the smallness parameter 1/2s where s is the spin magnitude. The long-wave spin fluctuations are governed by the nonlinear sigma model and are on the order of the smallness parameter 1/N, where N is the number of field components. We also have shown that the short wave spin fluctuations must be evaluated accurately and the continuum limit in time of the path integral must be performed after the summation over the frequencies ω.     

Invariant spin coherent states and the theory of the quantum antiferromagnet in a paramagnetic phase

A consistent theory of the Heisenberg quantum antiferromagnet in the disordered phase with short-range antiferromagnetic order was developed on the basis of the path integral for the spin coherent states. We presented the Lagrangian of the theory in the form that is explicitly invariant under rotations and found natural variables in terms of which one can construct a perturbation theory. The short-wavelength spin fluctuations are similar to the ones in spin-wave theory, and the long-wavelength spin fluctuations are governed by the nonlinear sigma model. We also demonstrated that the short-wavelength spin fluctuations should be considered accurately in the framework of the discrete version in time of the path integral. In the framework of our approach, we obtained the response function for the spin fluctuations for the whole region of the frequency ω and the wave vector k and calculated the free energy of the system.     

X-Y-Z模型——非各向同性反铁磁Heisenberg系统的自旋波解

给出了一个基于Holstein-primakoff变换的自旋波理论研究正方点阵X-Y-Z模型的基态和激发态性质的方案。通过引入宇称变换算子和正则变换,实现了Hamiltonian的对角化,在线性近似下发现存在两支色散关系不同的自旋波。同时,求得了展开至S^-1的修正项。 关键词：     

Atomic-scale contrast mechanism in atomic force microscopy

We present numerical results for the ground state and low-lying excited states of theS=1 antiferromagnetic Heisenberg chain with exchange and single-ion anisotropy for free boundary conditions and up to 16 spins. The excitation spectrum in the Néel and Haldane phases is interpreted successfully in terms of domain walls (i.e. solitons) only. We present evidence that the transition between these two phases is characterized by the condensation of the lowest soliton modes. The difference between periodic and open boundary conditions, in particular the relevance of open boundary conditions for numerical calculations on finite chains, is discussed.     

Semiclassical ordering in the large-N pyrochlore antiferromagnet

We study the semiclassical limit of the Sp(N) generalization of the pyrochlore lattice Heisenberg antiferromagnet by expanding about the N --> infinity saddlepoint in powers of a generalized inverse spin. To leading order, we write down an effective Hamiltonian as a series in loops on the lattice. Using this as a formula for calculating the energy of any classical ground state, we perform Monte Carlo simulations and find a unique collinear ground state. This state is not a ground state of linear spin-wave theory, and can therefore not be a physical (N = 1) semiclassical ground state.     

Holon kinetic energy in the RVB state

We have used a low energy variational RVB wave function to evaluate the kinetic energy of holons in the dilute limit. We report results on a 5×5 cluster; from the first 8 moments of the density of states, we estimate a lower band edge for the holon, which is fairly insensitive to details of the RVB wave function. This band edge is higher than the corresponding one for a hole in the Néel state, by about 0.08t, in the limitU/t.     

Hidden symmetry breaking and the Haldane phase inS=1 quantum spin chains

We study the phase diagram ofS=1 antiferromagnetic chains with particular emphasis on the Haldane phase. The hidden symmetry breaking measured by the string order parameter of den Nijs and Rommelse can be transformed into an explicit breaking of aZ ₂×Z ₂ symmetry by a nonlocal unitary transformation of the chain. For a particular class of Hamiltonians which includes the usual Heisenberg Hamiltonian, we prove that the usual Néel order parameter is always less than or equal to the string order parameter. We give a general treatment of rigorous perturbation theory for the ground state of quantum spin systems which are small perturbations of diagonal Hamiltonians. We then extend this rigorous perturbation theory to a class of diagonally dominant Hamiltonians. Using this theory we prove the existence of the Haldane phase in an open subset of the parameter space of a particular class of Hamiltonians by showing that the string order parameter does not vanish and the hiddenZ ₂×Z ₂ symmetry is completely broken. While this open subset does not include the usual Heisenberg Hamiltonian, it does include models other than VBS models.