  Strongly correlated Fermi systems are among the most intriguing and
fundamental systems in physics. We show that the herbertsmithite ZnCu3(OH)6Cl2
can be viewed as a new type of strongly correlated electrical insulator that
possesses properties of heavy-fermion metals with one exception: it resists the
flow of electric charge. We demonstrate that herbertsmithite's low temperature
properties are defined by a strongly correlated quantum spin liquid made with
such hypothetic particles as fermionic spinons which carry spin 1/2 and no
charge. Our calculations of its thermodynamic and relaxation properties are in
good agreement with recent experimental facts and allow us to reveal their
scaling behavior which strongly resembles that observed in heavy-fermion
metals. Analysis of the dynamic magnetic susceptibility of strongly correlated
Fermi systems suggests that there exist at least two types of its scaling.
