Large magnetic thermal conductivity induced by frustration in low-dimensional quantum magnets

We study the magnetic field-dependence of the thermal conductivity due to magnetic excitations in frustrated spin-1/2 Heisenberg chains. Near the saturation field, the system is described by a dilute gas of weakly interacting fermions (free-fermion fixed point). We show that in this regime the thermal conductivity exhibits a nonmonotonic behavior as a function of the ratio alpha = J(2)/J(1) between second- and first-nearest-neighbor antiferromagnetic exchange interactions. This result is a direct consequence of the splitting of the single-particle dispersion minimum into two minima that takes place at the Lifshitz point alpha = 1/4. Upon increasing a from zero, the inverse mass vanishes at alpha = 1/4 and it increases monotonically from zero for alpha >= 1/4. By deriving an effective low-energy theory of the dilute gas of fermions, we demonstrate that the Drude weight K-th of the thermal conductivity exhibits a similar dependence on a near the saturation field. Moreover, this theory predicts a transition between a two-component Tomonaga-Luttinger liquid and a vector-chiral phase at a critical value alpha = alpha(c) that agrees very well with previous density matrix renormalization group results. We also show that the resulting curve K-th (alpha) is in excellent agreement with exact diagonalization (ED) results. For the low-magnetic field regime, our ED results show that K-th (alpha) has a pronounced minimum at alpha similar or equal to 0.7. We also demonstrate that the thermal conductivity is significantly affected by the presence of magnetothermal coupling.