Within the memory function approach we study the thermal conductivity of the one-dimensional spin- $1∕2$ Heisenberg, as well as $XY$ model coupled to optic and acoustic phonons using exact diagonalization with the Lanczos technique and analytical evaluation, respectively. We find that the thermal conductivity of the two models is fairly similar, the enhancement found in the Heisenberg model mainly due to the larger energy current correlations. We also observe that the Wiedemann-Franz law is not obeyed in the $XY$ model, presumably due to the inelastic scattering processes.Within the memory function approach we study the thermal conductivity of the one-dimensional spin-$1∕2$ Heisenberg, as well as $XY$ model coupled to optic and acoustic phonons using exact diagonalization with the Lanczos technique and analytical evaluation, respectively. We find that the thermal conductivity of the two models is fairly similar, the enhancement found in the Heisenberg model mainly due to the larger energy current correlations. We also observe that the Wiedemann-Franz law is not obeyed in the $XY$ model, presumably due to the inelastic scattering processes.

Physical Review BDec 22, 200625 citations

Thermal transport in one-dimensional spin gap systems

E. Orignac, R. Chitra, R. Citro

We study thermal transport in one-dimensional spin systems both in the presence and absence of impurities. In the absence of disorder, all these spin systems display in the continuum limit a temperature-dependent Drude peak in the thermal conductivity. In gapless systems, the low-temperature Drude weight is proportional to temperature and to the central charge, which characterizes the conformal field theory that describes the system at low energies. On the other hand, the low-temperature Drude weight of spin gap systems shows an activated behavior modulated by a power law. For temperatures higher than the spin gap, one recovers the linear T behavior akin to gapless systems. For temperatures larger than the exchange coupling, the Drude weight decays as ${T}^{\ensuremath{-}2}.$ We argue that this behavior is a generic feature of quasi-one-dimensional spin gap systems with a relativistic like low-energy dispersion. We also consider the effect of a magnetic field on the Drude weight with emphasis on the commensurate-incommensurate transition induced by it. We then study the effect of nonmagnetic impurities on the thermal conductivity of the dimerized $\mathrm{XY}$ chain and the spin- $\frac{1}{2}$ two-leg ladder. Impurities destroy the Drude peak and the thermal conductivity exhibits a purely activated behavior at low temperature, with an activation gap renormalized by disorder. The relevance of these results for experiments is briefly discussed.We study thermal transport in one-dimensional spin systems both in the presence and absence of impurities. In the absence of disorder, all these spin systems display in the continuum limit a temperature-dependent Drude peak in the thermal conductivity. In gapless systems, the low-temperature Drude weight is proportional to temperature and to the central charge, which characterizes the conformal field theory that describes the system at low energies. On the other hand, the low-temperature Drude weight of spin gap systems shows an activated behavior modulated by a power law. For temperatures higher than the spin gap, one recovers the linear T behavior akin to gapless systems. For temperatures larger than the exchange coupling, the Drude weight decays as ${T}^{\ensuremath{-}2}.$ We argue that this behavior is a generic feature of quasi-one-dimensional spin gap systems with a relativistic like low-energy dispersion. We also consider the effect of a magnetic field on the Drude weight with emphasis on the commensurate-incommensurate transition induced by it. We then study the effect of nonmagnetic impurities on the thermal conductivity of the dimerized $\mathrm{XY}$ chain and the spin-$\frac{1}{2}$ two-leg ladder. Impurities destroy the Drude peak and the thermal conductivity exhibits a purely activated behavior at low temperature, with an activation gap renormalized by disorder. The relevance of these results for experiments is briefly discussed.

arXiv:cond-mat/0211633Physical review. B, Condensed matterApr 28, 200369 citations

Enhancement of the Thermal Conductivity in gaped Quantum Spin Chains

Keiji Saito, Seiji Miyashita

Jan 22, 20020 citations

Heat transport in quantum spin chains

Carlos Mejía-Monasterio, Hannu Christian Wichterich

arXiv:0709.1412The European Physical Journal Special TopicsDec 1, 200736 citations

Within the memory function approach we study the thermal conductivity of the one-dimensional spin-

1∕2

Heisenberg, as well as

XY

model coupled to optic and acoustic phonons using exact diagonalization with the Lanczos technique and analytical evaluation, respectively. We find that the thermal conductivity of the two models is fairly similar, the enhancement found in the Heisenberg model mainly due to the larger energy current correlations. We also observe that the Wiedemann-Franz law is not obeyed in the

XY

model, presumably due to the inelastic scattering processes.

\mathrm{XY}

chain and the spin-

\frac{1}{2}

two-leg ladder. Impurities destroy the Drude peak and the thermal conductivity exhibits a purely activated behavior at low temperature, with an activation gap renormalized by disorder. The relevance of these results for experiments is briefly discussed.