Linked-cluster Expansion Methods Research Articles

Linked cluster expansion of the many-body path integral

We develop an approach of calculating the many-body path integral based on the linked cluster expansion method. First, we derive a linked cluster expansion and we give the diagrammatic rules for calculating the free-energy and the pair distribution function $g(r)$ as a systematic power series expansion in the particle density. We also generalize the hypernetted-chain (HNC) equation for $g(r)$, known from its application to classical statistical mechanics, to a set of quantum HNC equations (QHNC) for the quantum case. The calculated $g(r)$ for distinguishable particles interacting with a Lennard-Jones potential in various attempted schemes of approximation of the diagrammatic series compares very well with the results of path integral Monte Carlo simulation even for densities as high as the equilibrium density of the strongly correlated liquid $^4$He. Our method is applicable to a wide range of problems of current general interest and may be extended to the case of identical particles and, in particular, to the case of the many-fermion problem.

Applications of the spin polaron theory at finite temperature

Some applications of the spin polaron theory at finite temperature are discussed in this paper. With the spin polaron Hamiltonian as the interaction term, the expression for the thermodynamic potential in the linked-cluster expansion method is determined and directly yields the finite temperature holon entropy and specific heat. A proposed generalization of the Wiedemann–Franz law is subsequently treated through the use of the relation for the holon specific heat.

A Different Theoretical Approach to the Spin Polaron Problem

Using the finite temperature (Matsubara) Green's function method, the spin polaron problem is investigated in the strong and weak coupling limits. The holon entropy and specific heat are calculated from the thermodynamic potential in the linked-cluster expansion method.

Comparison between linked-cluster expansion methods for the U(1) lattice gauge model in 2+1 dimensions

Comparisons are made between the t-expansion and the strong-coupling series expansion, as applied to the compact U(1) lattice gauge model in 2+1 dimensions. Connected moments of the Hamiltonian are calculated up to 28th order, extending previous results of Morningstar, and are used to form a t-expansion. The t-expansion is technically easier to calculate, and can give estimates of the axial string tension, which the series expansion cannot; but the series expansion gives better results for the mass gaps.

Comparison between linked-cluster expansion methods for the U(1) lattice gauge model in 2+1 dimensions.

Comparisons are made between two different linked-cluster expansion methods, namely, the t expansion and the strong-coupling series expansion, as applied to the compact U(1) lattice gauge model in 2+1 dimensions. Connected moments of the Hamiltonian are calculated up to 28th order, extending previous results of Morningstar, and are used to form a t expansion. The t expansion is technically easier to calculate, and can give estimates of the axial string tension, which the strong-coupling series expansion cannot; but the strong-coupling series expansion gives better results for the mass gaps. \textcopyright{} 1996 The American Physical Society.

Comparison between linked-cluster expansion methods for the Heisenberg antiferromagnet on the square lattice.

Comparison between linked-cluster expansion methods for the Heisenberg antiferromagnet on the square lattice.

Magnetic susceptibility of the strongly correlated Hubbard model.

Using the linked-cluster expansion method, we have calculated the uniform and the staggered susceptibility of a single-band Hubbard model. We make correction of previous results of Kubo and Zhao et al.

Electron-phonon thermodynamic potential and magnetism of a metal.

Starting from a thermodynamic potential of a metal which includes the contribution of phonons, Kim recently pointed out the importance of considering the electron-phonon interaction in understanding itinerant electron magnetism. In this paper we explicitly derive such a thermodynamic potential of a metallic electron-phonon system by using the linked cluster expansion method. An effort is made to include fully and consistently the effect of the exchange interaction between electrons, as well as the long-range Coulomb interaction. Our result is in accord with our anticipation and confirms the role of phonons in magnetism of metals.

Cluster expansion approach to non-abelian lattice gauge theory in (3 + 1)D (I). SU(2)

Linked cluster expansion methods are used to extend strong coupling series for the vacuum energy density, the axial string tension and the scalar mass gap for the SU(2) hamiltonian lattice gauge model in (3 + 1) dimensions. The related ELCE algorithm is used to calculate the string tension beyond its roughening transition. From the expected continuum scaling behaviour we estimate the string tension √ σ ∼ 0.6 Λ mom and the scalar glueball mass m s ∼ 2 Λ mom. Both estimates are somewhat lower than current Monte Carlo results but are not inconsistent in view of the large uncertainties.

Transverse susceptibility of spin-one Ising systems with uniaxial single-ion anisotropies

The transverse susceptibility of spin-one Ising systems with uniaxial single-ion anisotropies have been calculated using the linked-cluster expansion method. Series to the tenth order in the paramagnetic phase and to the eighth order in the ordered phase have been obtained for the FCC lattice with both easy-axis and hard-axis anisotropies of various magnitudes. It is found that the correlations of fluctuations play an essential role in predicting the true temperature behaviour of the transverse susceptibility.