a b s t r a c tStrongly correlated Fermi systems are fundamental systems in physics that are best studied experimentally, which until very recently have lacked theoretical explanations. This review discusses the construction of a theory and the analysis of phenomena occurring in strongly correlated Fermi systems such as heavy-fermion (HF) metals and two-dimensional (2D) Fermi systems. It is shown that the basic properties and the scaling behavior of HF metals can be described within the framework of a fermion condensation quantum phase transition (FCQPT) and an extended quasiparticle paradigm that allow us to explain the non-Fermi liquid behavior observed in strongly correlated Fermi systems. In contrast to the Landau paradigm stating that the quasiparticle effective mass is a constant, the effective mass of new quasiparticles strongly depends on temperature, magnetic field, pressure, and other parameters. Having analyzed the collected facts on strongly correlated Fermi systems with quite a different microscopic nature, we find these to exhibit the same non-Fermi liquid behavior at FCQPT. We show both analytically and using arguments based entirely on the experimental grounds that the data collected on very different strongly correlated Fermi systems have a universal scaling behavior, and materials with strongly correlated fermions can unexpectedly be uniform in their diversity. Our analysis of strongly correlated systems such as HF metals and 2D Fermi systems is in the context of salient experimental results. Our calculations of the non-Fermi liquid behavior, the scales and thermodynamic, relaxation and transport properties are in good agreement with experimental facts.

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Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics, whose realization in some compounds is still to be discovered. We show that herbertsmithite ZnCu3(OH)6Cl2 can be viewed as a strongly correlated Fermi system whose low temperature thermodynamic in magnetic fields is defined by a quantum critical spin liquid. Our calculations of its thermodynamic properties are in good agreement with recent experimental facts and allow us to reveal their scaling behavior which strongly resembles that observed in HF metals and 2D 3 He. An explanation of the rich behavior of strongly correlated Fermi systems still continues to be among the main problems of the condensed matter physics. One of the most interesting and puzzling issues in the research of strongly correlated Fermi systems is the non-Fermi liquid (NFL) behavior detected in their thermodynamic properties. Under the application of external fields, e.g. magnetic field B, the system can be driven to a Landau Fermi liquid behavior (LFL). Such a behavior was observed in quite different objects such as heavy-fermion (HF) metals [1, 2] and two-dimensional 3 He [2-5] Recently the herbertsmithite ZnCu 3 (OH) 6 Cl 2 has been exposed as a S = 1/2 kagome antiferromagnet [6] and new experimental investigations have revealed its unusual behavior [7][8][9]. Because of the electrostatic environment, Cu 2+ is expected to occupy the distorted octahedral kagome sites. Magnetic kagome planes Cu 2+ S = 1/2 are separated by nonmagnetic Zn 2+ layers. Observations have found no evidence of long range magnetic order or spin freezing down to temperature of 50 mK, indicating that ZnCu 3 (OH) 6 Cl 2 is the best model found of quantum kagome lattice [7][8][9][10]. The specific heat C, arising from the Cu spin system, at T < 1 K appears to be governed by a power law with an exponent which is less than or equal to 1. At the lowest explored temperature, namely over the temperature range 106 < T < 400 mK, C follows a linear law temperature dependence, C ∝ T , and for temperatures of a few Kelvin and higher, the specific heat becomes C(T ) ∝ T 3 and is dominated by the lattice contribution [7][8][9]. At low temperatures T ≤ 1, the strong magnetic field dependence of the specific heat C suggests that C is predominately magnetic in origin [7][8][9]. There are a number of papers suggesting that the S = 1/2 model on the kagome lattice can be viewed as the gapless critical spin liquid [7][8][9][13][14][15][16]. These facts allow us to test both the NFL and LFL behavior of ZnCu 3 (OH) 6 Cl 2 and to show that a Fermi quantum spin liquid formed in the herbertsmithite determines its low temperature thermodynamic properties.Contrary to the C ∝ T behavior [7,8], the observed spin liquids contribute a T 2 specific heat which in the model is not sensitive to an applied magnetic field [15,16]. Moreover the magnetic susceptibility χ(T ) of ZnCu 3 (OH) 6 Cl 2 shown in Fig.