Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons

TL;DR

This review explores recent advances in flat-band systems, focusing on spin and electronic models, including phase transitions, ferromagnetism, and potential experimental realizations, highlighting the rich physics arising from flat-band phenomena.

Contribution

It provides a comprehensive overview of recent developments in flat-band spin and electron systems, emphasizing new phenomena and theoretical insights.

Findings

Field-driven phase transitions in frustrated quantum antiferromagnets

Emergence of ground-state ferromagnetism in flat-band Hubbard models

Effect of slight dispersion on flat-band states

Abstract

In this review we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. Main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki-Hubbard model and the related Pauli-correlated percolation problem, as well as the dispersion-driven ground-state ferromagnetism in flat-band Hubbard systems. Closely related studies and possible experimental realizations of the flat-band physics are also described briefly.