In our review, we focus on the quantum spin liquid (QSL), defining the thermodynamic, transport, and relaxation properties of geometrically frustrated magnet (insulators) represented by herbertsmithite
. The review mostly deals with an historical perspective of our theoretical contributions on this subject, based on the theory of fermion condensation closely related to the emergence (due to geometrical frustration) of dispersionless parts in the fermionic quasiparticle spectrum, so-called flat bands. QSL is a quantum state of matter having neither magnetic order nor gapped excitations even at zero temperature. QSL along with heavy fermion metals can form a new state of matter induced by the topological fermion condensation quantum phase transition. The observation of QSL in actual materials such as herbertsmithite is of fundamental significance both theoretically and technologically, as it could open a path to the creation of topologically protected states for quantum information processing and quantum computation. It is therefore of great importance to establish the presence of a gapless QSL state in one of the most prospective materials, herbertsmithite. In this respect, the interpretation of current theoretical and experimental studies of herbertsmithite are controversial in their implications. Based on published experimental data augmented by our theoretical analysis, we present evidence for the the existence of a QSL in the geometrically frustrated insulator herbertsmithite
, providing a strategy for unambiguous identification of such a state in other materials. To clarify the nature of QSL in herbertsmithite, we recommend measurements of heat transport, low-energy inelastic neutron scattering, and optical conductivity
crystals subject to an external magnetic field at low temperatures. Our analysis of the behavior of
in herbertsmithite justifies this set of measurements, which can provide a conclusive experimental demonstration of the nature of its spinon-composed quantum spin liquid. Theoretical study of the optical conductivity of herbertsmithite allows us to expose the physical mechanisms responsible for its temperature and magnetic field dependence. We also suggest that artificially or spontaneously introducing inhomogeneity at nanoscale into
can both stabilize its QSL and simplify its chemical preparation, and can provide for tests that elucidate the role of impurities. We make predictions of the results of specified measurements related to the dynamical, thermodynamic, and transport properties in the case of a gapless QSL.
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