Coupled Cluster Method Calculations Of Quantum Magnets With Spins Of General Spin Quantum Number

TL;DR

This paper introduces a new high-order coupled cluster method formalism for quantum spin systems with arbitrary spin quantum number, demonstrating its accuracy through calculations on various one-dimensional models and comparing favorably with exact and DMRG results.

Contribution

The paper develops a novel high-order CCM formalism for general spin quantum numbers, enabling accurate ground state calculations for complex quantum magnets.

Findings

CCM results match exact solutions for spin-half models.

CCM accurately predicts the Haldane phase onset for spin-one.

Results are consistent with DMRG and Bethe Ansatz calculations.

Abstract

We present a new high-order coupled cluster method (CCM) formalism for the ground states of lattice quantum spin systems for general spin quantum number, $s$. This new ``general-$s$'' formalism is found to be highly suitable for a computational implementation, and the technical details of this implementation are given. To illustrate our new formalism we perform high-order CCM calculations for the one-dimensional spin-half and spin-one antiferromagnetic {\it XXZ} models and for the one-dimensional spin-half/spin-one ferrimagnetic {\it XXZ} model. The results for the ground-state properties of the isotropic points of these systems are seen to be in excellent quantitative agreement with exact results for the special case of the spin-half antiferromagnet and results of density matrix renormalisation group (DMRG) calculations for the other systems. Extrapolated CCM results for the sublattice magnetisation of the spin-half antiferromagnet closely follow the exact Bethe Ansatz solution, which contains an infinite-order phase transition at $\Delta=1$. By contrast, extrapolated CCM results for the sublattice magnetisation of the spin-one antiferromagnet using this same scheme are seen to go to zero at $\Delta \approx 1.2$, which is in excellent agreement with the value for the onset of the Haldane phase for this model. Results for sublattice magnetisations of the ferrimagnet for both the spin-half and spin-one spins are non-zero and finite across a wide range of $\Delta$, up to and including the Heisenberg point at $\Delta=1$.