arXiv subjects

Zheng Weihong

Publications and source records attributed to Zheng Weihong.

34 records · Page 2Linked to original sources

arXiv1998

Various series expansions for a Heisenberg antiferromagnet model for SrCu$_2$(BO$_3$)$_2$

We use a variety of series expansion methods at both zero and finite temperature to study an antiferromagnetic Heisenberg spin model proposed recently by Miyahara and Ueda for the quasi two-dimensional material SrCu$_2$(BO$_3$)$_2$. We confirm that this model exhibits a first-order quantum phase transition at T=0 between a gapped dimer phase and a gapless Néel phase when the ratio $x=J'/J$ of nearest and next-nearest neighbour interactions is varied, and locate the transition at $x_c=0.691(6)$. Using longer series we are able to give more accurate estimates of the model parameters by fitting to the high temperature susceptibility data.

cond-mat.str-el↗

arXiv1998

Studies of a 2-Chain Spin Ladder with Frustrating Second Neighbor Interactions

The Heisenberg model on a 2-chain spin-1/2 ladder with frustrating second neighbor interactions is studied by using series expansions about the Ising and dimer limits, numerical diagonalization, and by Abelian bosonization analysis. The phase diagram is determined, and pair correlations and the complete dispersion relations for the triplet spin-wave excitations are also computed.

cond-mat↗

arXiv1998

Meta-Plaquette Expansion for the Triplet Excitation Spectrum in CaV$_4$O$_9$

We study antiferromagnetic, $S=1/2$ Heisenberg models with nearest and second neighbor interactions on the one-fifth depleted square lattice which describes the spin degrees of freedom in the spin-gap system CaV$_4$O$_9$. The meta-plaquette expansion for the triplet excitation spectrum is extended to fifth order, and the results are compared with experimental data on CaV$_4$O$_9$. We attempt to locate the phase boundary between magnetically ordered and gapped phases.

cond-mat.str-el↗

arXiv1998

Studies of one- and two-hole states in the 2D t-J model via series expansions

We study one and two hole properties of the t-J model at half-filling on the square lattice using series expansion methods at T=0. The dispersion curve for one hole excitations is calculated and found to be qualitatively similar to that obtained by other methods, but the bandwidth for small $t/J$ is some 20% larger than given previously. We also obtain the binding energy and dispersion relation for two hole bound states. The lowest bound state as $t/J$ increases is found to be first d-wave, and then p-wave, in accordance with predictions based upon the Kohn-Luttinger effect. We also make a similar study for the $t-J_z$ model.

cond-mat.str-el↗

arXiv1998

Multi-layer S=1/2 Heisenberg antiferromagnet

The multi-layer $S={1\over 2}$ square lattice Heisenberg antiferromagnet with up to 6 layers is studied via various series expansions. For the systems with an odd number of coupled planes, the ground-state energy, staggered magnetization, and triplet excitation spectra are calculated via two different Ising expansions. The systems are found to have long range Néel order and gapless excitations for all ratios of interlayer to intralayer couplings, as for the single-layer system. For the systems with an even number of coupled planes, there is a second order transition point separating the gapless Neél phase and gapped quantum disordered spin liquid phase, and the critical points are located via expansions in the interlayer exchange coupling. This transition point is found to vary about inversely as the number of layers. The triplet excitation spectra are also computed, and at the critical point the normalized spectra appear to follow a universal function, independent of number of layers.

cond-mat.str-el↗

arXiv1997

Novel approach to description of spin liquid phases in low-dimensional quantum antiferromagnets

We consider quantum spin systems with dimerization, which at strong coupling have singlet ground states. To account for strong correlations, the excitations are described as dilute Bose gas of degenerate triplets with infinite on-site repulsion. This approach is applied to the two-layer Heisenberg model at zero temperature with general couplings. Our analytic results for the triplet gap, the excitation spectrum and the location of the quantum critical point are in excellent agreement with numerical results, obtained by dimer series expansions.

cond-mat.str-el↗

arXiv1997

Series Expansions for three-dimensional QED

Strong-coupling series expansions are calculated for the Hamiltonian version of compact lattice electrodynamics in (2+1) dimensions, with 4-component fermions. Series are calculated for the ground-state energy per site, the chiral condensate, and the masses of `glueball' and positronium states. Comparisons are made with results obtained by other techniques.

hep-lat↗

arXiv1997

Spin-S bilayer Heisenberg models: Mean-field arguments and numerical calculations

Spin-S bilayer Heisenberg models (nearest-neighbor square lattice antiferromagnets in each layer, with antiferromagnetic interlayer couplings) are treated using dimer mean-field theory for general S and high-order expansions about the dimer limit for S=1, 3/2,...,4. We suggest that the transition between the dimer phase at weak intraplane coupling and the Neel phase at strong intraplane coupling is continuous for all S, contrary to a recent suggestion based on Schwinger boson mean-field theory. We also present results for S=1 layers based on expansions about the Ising limit: In every respect the S=1 bilayers appear to behave like S=1/2 bilayers, further supporting our picture for the nature of the order-disorder phase transition.

cond-mat↗

arXiv1997

Series Expansions for the Massive Schwinger Model in Hamiltonian lattice theory

It is shown that detailed and accurate information about the mass spectrum of the massive Schwinger model can be obtained using the technique of strong-coupling series expansions. Extended strong-coupling series for the energy eigenvalues are calculated, and extrapolated to the continuum limit by means of integrated differential approximants, which are matched onto a weak-coupling expansion. The numerical estimates are compared with exact results, and with finite-lattice results calculated for an equivalent lattice spin model with long-range interactions. Both the heavy fermion and the light fermion limits of the model are explored in some detail.

hep-lat↗

arXiv1997

2D XXZ Model ground state Properties using an analytic Lanczos Expansion

We develop the formalism for calculating arbitrary expectation values for any extensive lattice Hamiltonian system using a new analytic Lanczos expansion, or plaquette expansion, and a recently proved exact theorem for ground state energies. The ground state energy, staggered magnetisation and the excited state gap of the 2D anisotropic antiferromagnetic Heisenberg Model are then calculated using this expansion for a range of anisotropy parameters and compared to other moment based techniques, such as the "t"-expansion, and spin-wave theory and series expansion methods. We find that far from the isotropic point all moment methods give essentially very similar results, but near the isotropic point the plaquette expansion is generally better than the others.

cond-mat.stat-mech↗

arXiv1997

Various series expansions for the bilayer S=1/2 Heisenberg antiferromagnet

Various series expansions have been developed for the two-layer, S=1/2, square lattice Heisenberg antiferromagnet. High temperature expansions are used to calculate the temperature dependence of the susceptibility and specific heat. At T=0, Ising expansions are used to study the properties of the Néel-ordered phase, while dimer expansions are used to calculate the ground-state properties and excitation spectra of the magnetically disordered phase. The antiferromagnetic order-disorder transition point is determined to be $(J_2/J_1)_c=2.537(5)$. Quantities computed include the staggered magnetization, the susceptibility, the triplet spin-wave excitation spectra, the spin-wave velocity, and the spin-wave stiffness. We also estimates that the ratio of the intra- and inter-layer exchange constants to be $J_2/J_1\simeq 0.07$ for cuprate superconductor $YBa_2Cu_3O_{6.2}$.

cond-mat.str-el↗

arXiv1996

Field Dependence of the Magnetization for the spin-ladder material Cu_2(C_5H_{12}N_2)_2Cl_4

We have developed a series expansion method for calculating the uniform magnetization, M, as a function of the applied field h for Heisenberg systems at T=0. The method involves introducing Ising anisotropy along the z-axis together with an applied uniform field along the x-axis. On extrapolation to the isotropic limit, one recovers the magnetization for the Heisenberg system with an applied field along the x-axis. This method circumvents the difficulties in developing perturbation theory associated with the commuting nature of the uniform field. The results developed for two-chain ladders appropriate for the material Cu_2(C_5H_{12}N_2)_2Cl_4 are in good agreement with the experimental data. In addition, uniform susceptibility is calculated by high temperature expansions and also compared with the experimental data.

cond-mat↗

arXiv1996

The Coupled Cluster Method in Hamiltonian Lattice Field Theory

The coupled cluster or exp S form of the eigenvalue problem for lattice Hamiltonian QCD (without quarks) is investigated. A new construction prescription is given for the calculation of the relevant coupled cluster matrix elements with respect to an orthogonal and independent loop space basis. The method avoids the explicit introduction of gauge group coupling coefficients by mapping the eigenvalue problem onto a suitable set of character functions, which allows a simplified procedure. Using appropriate group theoretical methods, we show that it is possible to set up the eigenvalue problem for eigenstates having arbitrary lattice momentum and lattice angular momentum.

hep-lat↗

arXiv1996

Studies of Quantum Spin Ladders at T=0 and at High Temperatures by Series Expansions

We have carried out extensive series studies, at T=0 and at high temperatures, of 2-chain and 3-chain spin-half ladder systems with antiferromagnetic intrachain and both antiferromagnetic and ferromagnetic interchain couplings. Our results confirm the existence of a gap in the 2-chain Heisenberg ladders for all non-zero values of the interchain couplings. Complete dispersion relations for the spin-wave excitations are computed. For 3-chain systems, our results are consistent with a gapless spectrum. We also calculate the uniform magnetic susceptibility and specific heat as a function of temperature. We find that as $T\to 0$, for the 2-chain system the uniform susceptibility goes rapidly to zero, whereas for the 3-chain system it approaches a finite value. These results are compared in detail with previous studies of finite systems.

cond-mat↗

arXiv1995

Universality for SU(2) Yang-Mills Theory in (2+1)D

The Green's Function Monte Carlo method of Chin et al is applied to SU(2) Yang-Mills theory in (2+1)D. Accurate measurements are obtained for the ground-state energy and mean plaquette value, and for various Wilson loops. The results are compared with series expansions and coupled cluster estimates, and with the Euclidean Monte Carlo results of Teper. A striking demonstration of universality between the Hamiltonian and Euclidean formulations is obtained.

hep-th↗

arXiv1992

Spin-Wave Theory and Finite-Size Scaling for the Heisenberg Antiferromagnet

Spin-wave perturbation theory for the Heisenberg antiferromagnet at zero temperature is used to compute the finite-lattice corrections to the ground state energy, the staggered magnetization and the energy gap. The dispersion relation, the spin-wave velocity and the bulk ground state energy to order $O(1/S^2)$ are also computed for the square lattice. The results agree very well with the predictions of Neuberger and Ziman and Fisher.

cond-mat↗