Abstract:
Experimental quest for the hypothetical "quantum spin liquid" state has recently
met a few promising candidate materials on certain geometrically frstrated lattices
such as the triangular and the kagome lattices. The former includes organic salts
κ-(ET)\(_2\)Cu\(_2\)(CN)\(_3\) and EtMe\(_3\)Sb[Pd(dmit)\(_2\)]\(_2\), while the latter includes herbersmithite
CuZn\(_3\)(OH)\(_6\)Cl\(_2\). These spin-1/2 compounds exhibit no magnetic ordering nor the spin
freezing down to very low temperature, while various physical quantities exhibit gapless
behaviors. We argue that these compounds might contain significant of quenched
randomness of varying origin, i.e., the freezing of the dielectric degrees of freedom in the
case of triangular organic salts and the random substitution of Cu\(^{2+}\) by Zn\(^{2+}\) in the case
of herbertsmithite, which might be essential in stabilizing the quantum spin-liquid-like
behaviors observed experimentally. We propose as a minimal model the S =1/2
antiferromagnetic Heisenberg model on the triangular and the kagome lattices with
a quenched randomness in the exchange interaction, and study both zero- and
finite-temperature properties of the model by an exact diagonalization method.
We then find that, when the randomness exceeds a critical value, the model exhibits
a quantum spin-liquid-like ground state with gapless behaviors, including the
temperature-linear specific heat. The low-temperature state is argued to be
a "random-singlet" or a "valence-bond-glass" state. The results seems to provide
a consistent explanation of the recent experimental observations.
[1] K. Watanabe, H. Kawamura, H. Nakano and T. Sakai, J. Phys. Soc. Jpn. 83, 034704 (2014)
[2] H. Kawamura, K. Watanabe and T. Shimokawa, J. Phys. Soc. Jpn. 83, 103704 (2014).