Scaling of electrical and thermal conductivities in an almost integrable chain

Many low-dimensional materials are well described by integrable one-dimensional models such as the Hubbard model of electrons or the Heisenberg model of spins. However, the small perturbations to these models required to describe real materials are expected to have singular effects on transport quantities: integrable models often support dissipationless transport, while weak nonintegrable terms lead to finite conductivities. We use matrix-product-state methods to obtain quantitative values of spin/electrical and thermal conductivities in an almost integrable gapless (XXZ-like) spin chain. At low temperatures, we observe power laws whose exponents are solely determined by the Luttinger liquid parameter. This indicates that our results are independent of the actual model under consideration.