Numerical and approximate analytical results for the frustrated spin-1/2 quantum spin chain

TL;DR

This paper combines analytical and numerical methods to analyze the ground state properties and phase transitions of the frustrated spin-1/2 chain described by the Majumdar-Ghosh model, providing detailed insights into its quantum phases.

Contribution

It introduces a coupled-cluster approach for the frustrated spin chain and compares its results with density matrix renormalisation group data, enhancing understanding of the phase behavior.

Findings

Ground state energy and pitch angle obtained via coupled-cluster method.

Numerical results from DMRG confirm analytical predictions.

Analysis of phase transition behavior near phase boundaries.

Abstract

We study the $T=0$ frustrated phase of the $1D$ quantum spin-$\frac 12$ system with nearest-neighbour and next-nearest-neighbour isotropic exchange known as the Majumdar-Ghosh Hamiltonian. We first apply the coupled-cluster method of quantum many-body theory based on a spiral model state to obtain the ground state energy and the pitch angle. These results are compared with accurate numerical results using the density matrix renormalisation group method, which also gives the correlation functions. We also investigate the periodicity of the phase using the Marshall sign criterion. We discuss particularly the behaviour close to the phase transitions at each end of the frustrated phase.