High-Order Coupled Cluster Method (CCM) Formalism 3: Finite-Size CCM. D.J.J. Farnell.

Recent developments of high-order CCM have been to extend existing formalism and codes to $s \ge \frac 12$ for both the ground and excited states, and independently to "generalised" expectation values for a wide range of one- and two-body spin operators. An advantage of the CCM is that the Goldstone linked-cluster theorem is obeyed at all levels of approximation and so it provides results in the infinite lattice limit $N \to \infty$ from the outset. However, recent results have also shown that the CCM can provide exact (symmetry-breaking) results for the spin-half linear-chain $J_1$ -- $J_2$ at the Majumdar-Ghosh point $J_2/J_1=0.5$ by identifying special solutions of the CCM equations for the usual Néel model state. Interestingly, the CCM provides exact (non-symmetry-breaking) results for systems in which small magnetic clusters become de-coupled from each other when the bonds connecting them tend to zero. These exact results involve the identification of "special solutions" of the CCM equations for the Néel state. An example of this is given by a spin-half system with nearest-neighbour bonds for an underlying lattice corresponding to the magnetic material CaV $_4$ O $_9$ (CAVO) in which one of the two different types of bonds on the lattice tend to zero. Larger finite-sized systems may be considered by appropriate choice of the unit cell and the bonds on it. We show here that exact diagonalisation results for ground-state energy and excitation energy gap for the spin-half and spin-one linear Heisenberg model on chains of length up to N=12 sites for s=1/2 and N=6 sites for s=1 with periodic boundary conditions are reproduced exactly using high-order CCM via this "brute-force" approach; i.e., one in which none of the translational or point-group symmetries of the finite lattice are used.Recent developments of high-order CCM have been to extend existing formalism and codes to $s \ge \frac 12$ for both the ground and excited states, and independently to "generalised" expectation values for a wide range of one- and two-body spin operators. An advantage of the CCM is that the Goldstone linked-cluster theorem is obeyed at all levels of approximation and so it provides results in the infinite lattice limit $N \to \infty$ from the outset. However, recent results have also shown that the CCM can provide exact (symmetry-breaking) results for the spin-half linear-chain $J_1$--$J_2$ at the Majumdar-Ghosh point $J_2/J_1=0.5$ by identifying special solutions of the CCM equations for the usual Néel model state. Interestingly, the CCM provides exact (non-symmetry-breaking) results for systems in which small magnetic clusters become de-coupled from each other when the bonds connecting them tend to zero. These exact results involve the identification of "special solutions" of the CCM equations for the Néel state. An example of this is given by a spin-half system with nearest-neighbour bonds for an underlying lattice corresponding to the magnetic material CaV$_4$O$_9$ (CAVO) in which one of the two different types of bonds on the lattice tend to zero. Larger finite-sized systems may be considered by appropriate choice of the unit cell and the bonds on it. We show here that exact diagonalisation results for ground-state energy and excitation energy gap for the spin-half and spin-one linear Heisenberg model on chains of length up to N=12 sites for s=1/2 and N=6 sites for s=1 with periodic boundary conditions are reproduced exactly using high-order CCM via this "brute-force" approach; i.e., one in which none of the translational or point-group symmetries of the finite lattice are used.

arXiv:1002.4396Feb 23, 20100 citations

High-Order Coupled Cluster Method (CCM) Formalism 1: Ground- and Excited-State Properties of Lattice Quantum Spin Systems with $s >= 1/2$ High-Order Coupled Cluster Method (CCM) Formalism 1: Ground- and Excited-State Properties of Lattice Quantum Spin Systems with $s >= 1/2$

DAMIAN J. J. FARNELL

The coupled cluster method (CCM) is a powerful and widely applied technique of modern-day quantum many-body theory. It has been used with great success in order to understand the properties of quantum magnets at zero temperature. This is due largely to the application of computational techniques that allow the method to be applied to high orders of approximation using localised approximation schemes, e.g., such as the LSUB $m$ scheme. In this article, the high-order CCM formalism for the ground and excited states of quantum magnetic systems are extended to those with spin quantum number $s \ge \frac 12$ . Solution strategies for the ket- and bra-state equations are also considered. Aspects of extrapolation of CCM expectation values are discussed and future topics regarding extrapolations are presented.The coupled cluster method (CCM) is a powerful and widely applied technique of modern-day quantum many-body theory. It has been used with great success in order to understand the properties of quantum magnets at zero temperature. This is due largely to the application of computational techniques that allow the method to be applied to high orders of approximation using localised approximation schemes, e.g., such as the LSUB$m$ scheme. In this article, the high-order CCM formalism for the ground and excited states of quantum magnetic systems are extended to those with spin quantum number $s \ge \frac 12$. Solution strategies for the ket- and bra-state equations are also considered. Aspects of extrapolation of CCM expectation values are discussed and future topics regarding extrapolations are presented.

arXiv:0909.1226Sep 7, 20090 citations

Generalized Variational Coupled-Cluster Formalism

Andrei Derevianko

APSMay 1, 20010 citations

Recent developments of high-order CCM have been to extend existing formalism and codes to

s \ge \frac 12

for both the ground and excited states, and independently to "generalised" expectation values for a wide range of one- and two-body spin operators. An advantage of the CCM is that the Goldstone linked-cluster theorem is obeyed at all levels of approximation and so it provides results in the infinite lattice limit

N \to \infty

from the outset. However, recent results have also shown that the CCM can provide exact (symmetry-breaking) results for the spin-half linear-chain

J_1

J_2

at the Majumdar-Ghosh point

J_2/J_1=0.5

by identifying special solutions of the CCM equations for the usual Néel model state. Interestingly, the CCM provides exact (non-symmetry-breaking) results for systems in which small magnetic clusters become de-coupled from each other when the bonds connecting them tend to zero. These exact results involve the identification of "special solutions" of the CCM equations for the Néel state. An example of this is given by a spin-half system with nearest-neighbour bonds for an underlying lattice corresponding to the magnetic material CaV

_4

_9

(CAVO) in which one of the two different types of bonds on the lattice tend to zero. Larger finite-sized systems may be considered by appropriate choice of the unit cell and the bonds on it. We show here that exact diagonalisation results for ground-state energy and excitation energy gap for the spin-half and spin-one linear Heisenberg model on chains of length up to N=12 sites for s=1/2 and N=6 sites for s=1 with periodic boundary conditions are reproduced exactly using high-order CCM via this "brute-force" approach; i.e., one in which none of the translational or point-group symmetries of the finite lattice are used.

High-Order Coupled Cluster Method (CCM) Formalism 1: Ground- and Excited-State Properties of Lattice Quantum Spin Systems with

s >= 1/2

m

scheme. In this article, the high-order CCM formalism for the ground and excited states of quantum magnetic systems are extended to those with spin quantum number

s \ge \frac 12

. Solution strategies for the ket- and bra-state equations are also considered. Aspects of extrapolation of CCM expectation values are discussed and future topics regarding extrapolations are presented.