The ground state energy of the frustrated ferromagnetic spin chain near the transition point

TL;DR

This paper investigates the quantum ground state energy of a one-dimensional frustrated ferromagnetic spin chain near a critical transition point, using bosonization and Green's function methods to derive and analyze energy corrections.

Contribution

It introduces a combined bosonization and Green's function approach to analytically derive the quantum correction to the ground state energy near the transition point.

Findings

Derived an integral expression for quantum correction to ground state energy.

Numerically confirmed the critical behavior as proportional to -8γ^2.

Analyzed the transition from ferromagnetic to singlet ground state.

Abstract

The one-dimensional quantum spin-1/2 model with nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is considered. The Hamiltonian is first bosonized by using the linear spin wave approximation, and then is treated by using the Green's function approach. An integral expression of the quantum correction to the classical ground state energy is derived. The critical behavior of the ground state energy in the vicinity of the transition point from the ferromagnetic to the singlet ground state is analyzed by numerical calculation, and the result is $-8\gamma^2$.