Spin models of quasi-1D quantum ferrimagnets with competing interactions

TL;DR

This paper surveys recent theoretical studies on quasi-1D quantum ferrimagnets modeled by Heisenberg spin systems, focusing on complex interactions, phase diagrams, and quantum phase transitions in various frustrated spin chains and ladders.

Contribution

It provides a comprehensive overview of recent advances in understanding quantum ferrimagnets with competing interactions, highlighting models, phase diagrams, and open problems.

Findings

Rich quantum phase diagrams identified in various models

Examples of magnetic-paramagnetic quantum phase transitions

Open problems in the field discussed

Abstract

We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets. The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated $J_1-J_2$ chain with alternating (1,1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration. As a rule, discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase transitions. A number of open problems in the reviewed research area are discussed.