Contrary to the original expectation, Na2IrO3 is not a Kitaev's quantum spin liquid (QSL) but shows a zigzag-type antiferromagnetic order in experiments. Here, we propose experimental clues and criteria to measure how a material in hand is close to the Kitaev's QSL state. For this purpose, we systematically study thermal and spin excitations of a generalized Kitaev-Heisenberg model studied by Chaloupka, Phys. Rev. Lett. 110, 097204 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.097204 and an effective ab initio Hamiltonian for Na2IrO3 proposed by Yamaji, Phys. Rev. Lett. 113, 107201 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.107201, by employing a numerical diagonalization method. We reveal that closeness to the Kitaev's QSL is characterized by the following properties, besides trivial criteria such as reduction of magnetic ordered moments and Néel temperatures. (1) Two peaks in the temperature dependence of specific heat at T and Th caused by the fractionalization of spin to two types of Majorana fermions. (2) In between the double peak, a prominent plateau or shoulder pinned at R2ln2 in the temperature dependence of entropy, where R is the gas constant. (3) Failure of the linear spin wave approximation at the low-lying excitations of dynamical structure factors. (4) Small ratio T/Th close to or less than 0.03. According to the proposed criteria, Na2IrO3 is categorized to a compound close to the Kitaev's QSL, and is proven to be a promising candidate for the realization of the QSL if the relevant material parameters can further be tuned by making thin film of Na2IrO3 on various substrates or applying axial pressure perpendicular to the honeycomb networks of iridium ions. Applications of these characterization to (Na1-xLix)2IrO3 and other related materials are also discussed.
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