Linked-cluster Series Expansion Research Articles

Series expansion study of spin-1 Heisenberg antiferromagnet with easy-plane single-ion anisotropy

Sixth-order series expansions for the free energy and the staggered susceptibility of a spin-1 Heisenberg antiferromagnet with easy-plane single-ion anisotropy on three-dimensional bipartite lattices have been calculated from the linked-cluster series expansion. We obtain accurate estimate of T N vs D phase diagram separating paramagnetic and planar antiferromagnetic phases. The critical point and critical exponent of the quantum phase transition occurring at T = 0 are also determined. The results are compared with related works.

Magnetic properties of spin-1 Heisenberg antiferromagnet with easy-axis single-ion anisotropy in three dimensions: Linked-cluster series expansion approach

The magnetic properties of spin-1 Heisenberg and Ising antiferromagnet with easy-axis single-ion anisotropy are studied in both ordered phase and disordered phase by using the linked-cluster series expansion method. We calculate the seventh-order series for the free energy and staggered susceptibility and the sixth-order series for the staggered magnetization on three-dimensional bipartite lattices. We obtain accurate estimate of the N\'eel temperature, the critical exponent $\ensuremath{\gamma}$, and the staggered magnetization. The effect of quantum and thermal spin fluctuations on the magnetic ordering of the system is discussed.

Magnetic order in coupled spin-half and spin-one Heisenberg chains in an anisotropic triangular-lattice geometry

We study spin-half and spin-one Heisenberg models in the limit where one-dimensional (1D) linear chains, with exchange constant ${J}_{1}$, are weakly coupled in an anisotropic triangular-lattice geometry. Results are obtained by means of linked-cluster series expansions at zero temperature around different magnetically ordered phases. We study the noncollinear spiral phases that arise classically in the model and the collinear antiferromagnet that has been recently proposed for the spin-half model by Starykh and Balents [Phys. Rev. Lett. 98, 077205 (2007)] using a renormalization group approach. We find some evidence that such phases can be stabilized in the spin-half model for arbitrarily small coupling between the chains, though convergence of the sublattice-magnetization series remains unsatisfactory. For vanishing coupling between the chains the energy of each phase must approach that of decoupled linear chains. With increasing interchain coupling, the noncollinear phase appears to have a lower energy in our calculations. For the spin-one chain, we find that there is a critical interchain coupling needed to overcome the Haldane gap. When spin-one chains are coupled in the frustrated triangular-lattice geometry, the critical coupling required to close the Haldane gap is enhanced by an order of magnitude compared to unfrustrated interchain couplings in the square-lattice geometry. The collinear phase is not obtained for the spin-one Heisenberg model.

Phase diagram of the bccS=12Heisenberg antiferromagnet with first and second neighbor exchange

We use linked-cluster series expansions, both at $T=0$ and high temperature, to analyze the phase structure of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet with competing first- and second-neighbor interactions on the three-dimensional body-centered-cubic lattice. At zero temperature we find a first-order quantum phase transition at ${J}_{2}{/J}_{1}\ensuremath{\simeq}0.705\ifmmode\pm\else\textpm\fi{}0.005$ between ${\mathrm{AF}}_{1}$ (Ne\'el) and ${\mathrm{AF}}_{2}$ ordered phases. The high-temperature series yield quite accurate estimates of the bounding critical line for the ${\mathrm{AF}}_{1}$ phase, and an apparent critical line for the ${\mathrm{AF}}_{2}$ phase, with a bicritical point at ${J}_{1}{/J}_{2}\ensuremath{\simeq}0.71,$ ${kT/J}_{1}\ensuremath{\simeq}0.34.$ The possibility that this latter transition is of first order cannot be excluded.

Mixed-spinS=(12,1)XXZferrimagnet at zero temperature: Cluster series expansions

Linked cluster series expansions about the Ising limit are used to study ground-state properties, viz. ground-state energy, magnetization, and excitation spectra, for mixed-spin $S=(\frac{1}{2},1)$ quantum ferrimagnets on simple bipartite lattices in 1, 2, and 3 dimensions. Results are compared to second-order spin-wave theory and, in general, excellent agreement is obtained.

Zero-temperature series expansions for the Kondo lattice model at half filling

We present new results for the Kondo lattice model of strongly correlated electrons, in 1-, 2-, and 3-dimensions, obtained from high-order linked-cluster series expansions. Results are given for varies ground state properties at half-filling, and for spin and charge excitations. The existence and nature of the predicted quantum phase transition are explored.

Two-hole and four-hole bound states in at-J ladder at half-filling

The two-hole excitation spectrum of the t-J ladder at half-filling is studied using linked-cluster series expansion methods. A rich spectrum of bound states emerges, particularly at small $t/J$. Their dispersion relations and coherence lengths are computed, along with the threshold behaviour as the bound states merge into the continuum. A class of 4-hole bound states is also studied, leading to the conclusion that phase separation occurs for $t/J \lesssim 0.5$, in agreement with other studies.

Linked cluster series expansions for two-particle bound states

We develop strong-coupling series expansion methods to study two-particle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the two-particle subspace. We explicitly consider an orthogonality transformation to generate this block diagonalization, and find that maintaining orthogonality is crucial for systems where the ground state and the two-particle subspace are characterized by identical quantum numbers. We discuss the solution of the two-particle Schrodinger equation by using a finite lattice approach in coordinate space or by an integral equation in momentum space. These methods allow us to precisely determine the low-lying excitation spectra of the models at hand, including all two-particle bound/antibound states. Further, we discuss how to generate series expansions for the dispersions of the bound/antibound states. These allow us to employ series extrapolation techniques, whereby binding energies can be determined even when the expansion parameters are not small. We apply the method to the ~111!-dimensional transverse Ising model and the two-leg spin- 1 2 Heisenberg ladder. For the latter model, we also calculate the coherence lengths and determine the critical properties where bound states merge with the two-particle continuum.

Local spin correlations in Heisenberg antiferromagnets

We use linked cluster series expansion methods to estimate the values of various short distance correlation functions in $S=1/2$ Heisenberg antiferromagnets at T=0, for dimension $d=1,2,3$. The method incorporates the possibility of spontaneous symmetry breaking, which is manifest in $d=2,3$. The results are important in providing a test for approximate theories of the antiferromagnetic ground state.

Formula omitted] Heisenberg antiferromagnet in a magnetic field: linked-cluster series expansion technique

Eighth-order high-temperature series expansions for the free energy, the magnetization and the staggered susceptibility of a spin- 1 2 Heisenberg antiferromagnet in a magnetic field on three-dimensional bipartite lattices have been derived from the linked-cluster series expansion. These series have been analyzed using Padé approximants to obtain the critical temperature and the magnetization at the critical temperature as a function of applied magnetic field. The phase diagram in the critical magnetic field versus critical temperature plane is obtained for the body-centered cubic lattice in the low-field region.

Magnetic phase diagram of the half-filled three-dimensional Hubbard model

Magnetic properties of the half-filled Hubbard model on three-dimensional bipartite lattices have been studied by using the linked-cluster series expansion method. The series for the free energy and the staggered susceptibility have been calculated as a function of \ensuremath{\mathrm{B}}t for three-dimensional bipartite lattices for an arbitrary value of the Coulomb interaction U. We obtain a transition from a paramagnetic to an antiferromagnetic U/t-${\mathrm{T}}_{\mathrm{N}}$ /t phase diagram from the divergence of the staggered susceptibility series. Comparisons with Monte Carlo simulation, Onsager reaction field result of an effective spin Hamiltonian, and large-U Heisenberg high-temperature solutions are made.

Magnetic properties of spin-one ferromagnets with an arbitrary crystal-field potential

The magnetic properties of spin-one Heisenberg ferromagnets with general crystal field potential are investigated using the linked cluster expansion. A modified Wick reduction theorem is used to calculate the τ integrals occuring in the series expansion. The results of the linked cluster series expansion cover both the ordered and disordered phases of a system. The dependence of the critical temperature on the crystal-field potentials and the magnetization as a function of temperature and crystal-field potentials are shown. A comparison is made with the prediction in the mean-field approximation.

Quantum fluctuations in easy-plane spin-one ferromagnet

The magnetic properties of easy-plane spin-one Heisenberg ferromagnet, H=D∑i(Six)2 −J∑(i,j)Si⋅Sj−h∑iSiz, are investigated using the linked cluster series expansion. The results of the linked cluster series expansion method cover the whole range of temperatures, both magnetically ordered and disordered phases. The order parameter is included in correlations of spin fluctuation and solved self-consistently to high orders. The magnetization as a function of temperature for a given value of easy-plane anisotropy is shown. The observed values of magnetization from the linked cluster series expansion are appreciably depressed from their mean-field approximation values due to the quantum and thermal fluctuations. The effects of the quantum fluctuation on the magnetic ordering in three-dimensional (3D) systems are discussed.

Linked-cluster series expansion for the spin-one Heisenberg model with easy-axis anisotropy: specific heat

The linked-cluster series expansion technique is used to calculate the specific heat series of the spin-one Heisenberg model with easy-axis anisotropy on the FCC lattice. Series coefficients through sixth order in the interaction parameter are obtained. Examples of the temperature dependence of the specific heat in both ferromagnetic and paramagnetic phase are given. Comparison is made with the mean-field approximation and with a Green function theory.

Linked-cluster series expansion for the spin-one Heisenberg model with easy-axis single-ion anisotropy

An efficient method for producing linked-cluster series expansions is illustrated by calculating a sixth-order series for the free energy of the spin-one Heisenberg model with an easy-axis single-ion potential which is treated exactly. This method makes use of the multiple-site Wick reduction process in a computer algebra system. A description of the method is given, and then a sixth-order series for the susceptibility in the paramagnetic phase for general lattice and magnetisation series for face-centred cubic, body-centred cubic and simple cubic lattices are presented.

Linked-cluster series-expansion technique for quantum spin systems.

The linked-cluster series expansion is developed for use on models of quantum spin systems with single-ion potentials. A Wick-like theorem is used to calculate the \ensuremath{\tau} integrals occurring in the series expansion. Such a new approach can deal with many realistic models of magnetic materials and will yield high-accuracy results in both ordered and disordered phases. These developments are illustrated by calculating the first seven terms of the linked-cluster series for the free energy, susceptibility, specific heat, and spontaneous magnetization of the spin-1 anisotropic Heisenberg model with a uniaxial single-ion potential. Thermodynamic properties of the system in both paramagnetic and magnetically ordered phases are discussed including the magnetization and susceptibility as functions of temperature, the critical exponents \ensuremath{\beta} and \ensuremath{\gamma}, and the existence of tricritical and bicritical points.

Linked cluster series expansion and phase transitions in complex models

We show that the use of the linked-cluster series expansion aided by the extrapolation techniques is an effective method in the study of complex models which display first-order phase transitions as well as second-order phase transitions. The Blume–Capel model is used for the demonstration.

Methods in hamiltonian lattice field theory (II). Linked-cluster expansions

The linked cluster series expansion proposed by Nickel is extended to the ground state and axial string tension of lattice gauge theory. Proofs of these expansions and applications to Z 2 and U(1) gauge theory in 2 + 1 dimensions are presented. We also propose a new finite cluster scaling method based on the linked-cluster expansion and test it against known results for Z 2 gauge theory. The utility of the method in studying more complicated lattice gauge theories is emphasized.