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 Lu3Cu2Sb3O14 and quasi-one dimensional (1D) quantum spin liquid in both YbAlO3 and Cu(C4H4N2)(NO3)2 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 α-YbAl1-xFexB4, with x=0.014, and on its sister compounds β-YbAlB4 and YbCo2Ge4, 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 α-YbAl1-xFexB4 and in its sister compounds β-YbAlB4 and YbCo2Ge4 emerge, as well as establish connection of these (HF) metals with insulators Lu3Cu2Sb3O14, Cu(C4H4N2)(NO3)2 and YbAlO3. 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.