In the insulator herbertsmithite, an exotic strongly correlated quantum spin liquid (SCQSL) is formed with such hypothetic particles as fermionic spinons carrying spin 1/2 and no charge.  The key features of our findings are the presence of spin-charge separation and SCQSL formed with itinerant spinons in herbertsmithite. We show that herbertsmithite represents a fascinating experimental example of a new strongly correlated insulator.  Thus, herbertsmithite can be viewed as a new type of strongly correlated electrical insulator that possesses properties of heavy-fermions metals with one exception: it resists the flow of electric charge. Presently herbertsmithite ZnCu₃(OH)₆Cl₂ has been exposed as  Heisenberg antiferromagnet on a perfect kagome lattice [1]. A frustration of simple kagome lattice leads to a dispersionless topologically protected branch of the spectrum with zero excitation energy known as the flat band. In this  case the fermion condensation quantum phase transition can be considered as quantum critical point of the herbertsmithite QSL composed of chargeless fermions with S=1/2 occupying the corresponding Fermi sphere [2-3]. The low-temperature specific heat follows the linear temperature dependence. These results suggest that the SCQSL state with essentially gapless excitations is realized in Herbertsmithite. In our report, we analyze the thermodynamic and relaxation properties, and unveil the fundamental properties of QSL, forming SCQSL. Taking into account that inelastic neutron scattering is a unique tool for studying dynamic magnetic properties, we present a theory of the dynamic magnetic susceptibility of quantum spin liquid collected in inelastic neutron scattering measurements. The obtained results are in good agreement with experimental facts collected on herbertsmithite ZnCu₃(OH)₆Cl₂ and on heavy-fermion  metals, and allow us to predict a new scaling in magnetic fields of the dynamic susceptibility. Under the application of strong magnetic fields quantum spin liquid becomes completely polarized. We show that this polarization can be viewed as a manifestation of gapped excitations when investigating the spin-lattice relaxation rate.  Magnetic response of herbertsmithite displays scaling relation in the bulk ac susceptibility, with the low temperature heat capacity strongly depending on magnetic field. This scaling is seen in certain heavy-fermion metals as a signature of proximity to a quantum critical point.

1.  L. Balents, Nature 464, 199 (2010).

2. V. R. Shaginyan, M.Ya. Amusia, A.Z. Msezane, and K.G. Popov, Physics Reports 492, 31 (2010).

3. V. R. Shaginyan, A. Z. Msezane, and K. G. Popov,  Phys. Rev. B 84, 060401(R) (2011).