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

Abstract

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 $\ensuremath{\alpha}={J}_{2}/{J}_{1}$ 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 $\ensuremath{\alpha}=1/4$. Upon increasing $\ensuremath{\alpha}$ from zero, the inverse mass vanishes at $\ensuremath{\alpha}=1/4$ and it increases monotonically from zero for $\ensuremath{\alpha}\ensuremath{\ge}1/4$. By deriving an effective low-energy theory of the dilute gas of fermions, we demonstrate that the Drude weight ${K}_{\mathrm{th}}$ of the thermal conductivity exhibits a similar dependence on $\ensuremath{\alpha}$ 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 $\ensuremath{\alpha}={\ensuremath{\alpha}}_{c}$ that agrees very well with previous density matrix renormalization group results. We also show that the resulting curve ${K}_{\mathrm{th}}(\ensuremath{\alpha})$ is in excellent agreement with exact diagonalization (ED) results. For the low-magnetic field regime, our ED results show that ${K}_{\mathrm{th}}(\ensuremath{\alpha})$ has a pronounced minimum at $\ensuremath{\alpha}\ensuremath{\simeq}0.7$. We also demonstrate that the thermal conductivity is significantly affected by the presence of magnetothermal coupling.