The Fascinating World of Low-Dimensional Quantum Spin Systems: Ab Initio Modeling.

Tanusri Saha-Dasgupta

doi:10.3390/molecules26061522

Abstract

In recent times, ab initio density functional theory has emerged as a powerful tool for making the connection between models and materials. Insulating transition metal oxides with a small spin forms a fascinating class of strongly correlated systems that exhibit spin-gap states, spin–charge separation, quantum criticality, superconductivity, etc. The coupling between spin, charge, and orbital degrees of freedom makes the chemical insights equally important to the strong correlation effects. In this review, we establish the usefulness of ab initio tools within the framework of the N-th order muffin orbital (NMTO)-downfolding technique in the identification of a spin model of insulating oxides with small spins. The applicability of the method has been demonstrated by drawing on examples from a large number of cases from the cuprate, vanadate, and nickelate families. The method was found to be efficient in terms of the characterization of underlying spin models that account for the measured magnetic data and provide predictions for future experiments.

Highlights

Compounds that have a dimensionality of less than three dimensions have long caught the attention of researchers due to their unconventional properties
It is worth mentioning at this point that other attempts at ab initio modeling of low-dimensional quantum spin systems exist, which use a variety of methods, such as the extended Huckel tight-binding method (EHTB) [21], tight-binding fitting of the density function theory (DFT) band structure in terms of Slater–Koster parametrization, and total energy calculations
The strong correlation effect that dictates the properties of quantum spin systems, prohibits the direct usage of the DFT for this purpose

Summary

Introduction

Compounds that have a dimensionality of less than three dimensions have long caught the attention of researchers due to their unconventional properties. Within the limited scope of the present review, we discuss the theoretical attempts within the framework of ab initio density functional theory coupled with the solution of a model Hamiltonian derived based on ab initio inputs, which is applied to understanding and predictions of low-dimensional quantum spin compounds. It is worth mentioning at this point that other attempts at ab initio modeling of low-dimensional quantum spin systems exist, which use a variety of methods, such as the extended Huckel tight-binding method (EHTB) [21], tight-binding fitting of the density function theory (DFT) band structure in terms of Slater–Koster parametrization, and total energy calculations. In addition to quantum Monte Carlo (QMC) and exact diagonalization, methods like the density matrix renormalization group (DMRG) [27], bond-operator theory, variational Ansätze, etc. have been used for solving the spin Hamiltonian

Theoretical Framework

Vanadates

Nickelates

Findings

Summary and Outlook