Thermal Transport in a one-dimensional Z$_{2}$ Spin Liquid
  We study the dynamical thermal conductivity of the Kitaev spin model on a two-leg ladder. In contrast to conventional integrable one-dimensional spin systems, we show that heat transport is completely dissipative. This is a direct consequence of fractionalization of spins into mobile Majorana matter and a static $Z_{2}$ gauge field, which acts as an emergent thermally activated disorder. Our finding rests on three complementary calculations of the current correlation function, comprising a phenomenological mean-field treatment of thermal gauge fluctuations, a complete summation over all gauge sectors, as well as exact diagonalization of the original spin model. The results will also be contrasted against the conductivity discarding gauge fluctuations. 
Alexandros Metavitsiadis and Wolfram Brenig
cond-mat.str-el