Simulations of pure and doped low-dimensional spin-1/2 gapped systems

TL;DR

This paper numerically investigates low-dimensional spin-1/2 systems with antiferromagnetic interactions, focusing on the formation of spin gaps due to geometrical effects, frustration, and impurity doping, using Exact Diagonalisation methods.

Contribution

It introduces numerical techniques including Exact Diagonalisation and mean-field extensions to study frustrated spin systems and their disordered phases.

Findings

Frustration plays a key role in spin gap formation.

Impurity doping affects the magnetic properties of Spin-Peierls systems.

Numerical methods effectively analyze complex low-dimensional quantum spin systems.

Abstract

Low dimensional spin-1/2 systems with antiferromagnetic interactions display very innovative features, driven by strong quantum fluctuations. In particular, geometrical effects or competing magnetic interactions can give rise to the formation of a spin gap between the singlet ground state and the first excited triplet state. In this chapter, we focus on the numerical investigation of such systems by Exact Diagonalisation methods and some extensions of it including a simultaneous mean-field treatment of some perturbative couplings. After a presentation of the Lanczos algorithm and a description of the space group symmetries, we give a short review on some pure low-dimensionnal frustrated spin gapped systems. In particular, we outline the role of the magnetic frustration in the formation of disordered phase. A large part is also devoted to frustrated Spin-Peierls systems for which the role of interchain couplings as well as impurity doping effects has been studied numerically.