Frustration and quantum criticality

Abstract

This review article is devoted to the interplay between frustrated magnetism and quantum critical phenomena, covering both theoretical concepts and ideas as well as recent experimental developments in correlated-electron materials. The first part deals with local-moment magnetism in Mott insulators and the second part with frustration in metallic systems. In both cases, frustration can either induce exotic phases accompanied by exotic quantum critical points or lead to conventional ordering with unconventional crossover phenomena. In addition, the competition of multiple phases inherent to frustrated systems can lead to multi-criticality.

Quantum topological transitions and spinons in metallic ferro- and antiferromagnets

“…QPT are treated in both usual paramagnetic and (in the presence of frustrations) exotic spin-liquid states [3]. However, concepts of exotic QPT can be applied to ferromagnetic (FM) and antiferromagnetic (AFM) phases too.…”

“…However, concepts of exotic QPT can be applied to ferromagnetic (FM) and antiferromagnetic (AFM) phases too. Here belong also problems of magnetism in high-T c cuprates [2] and Kondo lattices [3,4].…”

Scaling theory of magnetism in frustrated Kondo lattices

“…This picture is similar to that of Refs. [11,13,19] treating the critical non-Fermi-liquid FL * phase which is an analogue of spin-liquid state. However, occurrence of a (secondary) itinerant magnetic ordering in the low-temperature (strong coupling) regime is not excluded, as discussed in [11,19].…”

“…As noted in the review [13], frustrations yield the general tendency to reduce energy scales, which is manifest in electron or magnon bands of reduced width and reduced coherence scales, so that essential many-body renormalizations occur even in the antiferromagnetic (AFM) phase. In the present work, we investigate this problem in the renomalization group approach starting from weak coupling.…”

Topological nature of Hubbard bands in strongly correlated systems

“…Here, orbital-selective (partial) Mott transition in one band takes place which is a quantized change of Fermi surface, i.e. transition from large to small Fermi surface [22], which is related to formation of the Hubbard subbands.…”