Strongly Correlated Quantum Spin Liquids versus Heavy Fermion Metals: A Review

This review considers the topological fermion condensation quantum phase transition (FCQPT) that explains the complex behavior of strongly correlated Fermi systems, such as frustrated insulators with quantum spin liquid and heavy fermion metals. The review contrasts theoretical consideration with recent experimental data collected on both heavy fermion metals (HF) and frustrated insulators. Such a method allows to understand experimental data. We also consider experimental data collected on quantum spin liquid in [Formula: see text] and quasi-one dimensional (1D) quantum spin liquid in both [Formula: see text] and [Formula: see text] with the aim to establish a sound theoretical explanation for the observed scaling laws, Landau Fermi liquid (LFL) and non-Fermi-liquid (NFL) behavior exhibited by these frustrated insulators. The recent experimental data on the heavy-fermion metal [Formula: see text] [Formula: see text] , with [Formula: see text] , and on its sister compounds [Formula: see text] [Formula: see text] and [Formula: see text] , carried out under the application of magnetic field as a control parameter are analyzed. We show that the thermodynamic and transport properties as well as the empirical scaling laws follow from the fermion condensation theory. We explain how both the similarity and the difference in the thermodynamic and transport properties of [Formula: see text] [Formula: see text] and in its sister compounds [Formula: see text] [Formula: see text] and [Formula: see text] emerge, as well as establish connection of these (HF) metals with insulators [Formula: see text] , [Formula: see text] and [Formula: see text]. We demonstrate that the universal LFL and NFL behavior emerge because the HF compounds and the frustrated insulators are located near the topological FCQPT or are driven by the application of magnetic fields.