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Transport properties of the XX chain in a staggered magnetic field

鈴木　秀則

Published Dec 24, 2016• 0 citations
Publisher

Abstract

The thermal and spin Drude weights of the XX spin chain in staggered and uniform magnetic fields are exactly calculated and the low temperature behaviours of these quantities are derived.The temperature dependence of the thermal Drude weight shows double-peak behaviour as a result of the energy gap caused by the staggered magnetic field.The magnetic Seebeck coefficient is also analyzed in detail to investigate the magnetothermal effect.

DOI
10.15006/0002002751

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The thermal and spin Drude weights of the XX spin chain in staggered and uniform magnetic fields are exactly calculated and the low temperature behaviours of these quantities are derived.The temperature dependence of the thermal Drude weight shows double-peak behaviour as a result of the energy gap caused by the staggered magnetic field.The magnetic Seebeck coefficient is also analyzed in detail to investigate the magnetothermal effect.
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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 XY\mathrm{XY}XY chain and the spin-12\frac{1}{2}21​ 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.
Anomalous magnetothermal effects are discussed in the spin-1/2 Heisenberg chain.The energy current is related to one of the non-trivial conserved quantities underlying integrability and therefore both the diagonal and off diagonal dynamical correlations of spin and energy current diverge.The energy-energy and spin-energy current correlations at finite temperatures are exactly calculated by a lattice path integral formulation.The low-temperature behavior of the thermomagnetic (magnetic Seebeck) coefficient is also discussed.Due to effects of strong correlations, we observe the magnetic Seebeck coefficient changes sign at certain interaction strengths and magnetic fields.
Thermodynamic properties of the S=1/2 Heisenberg chain in transverse staggered magnetic field H^y_s and uniform magnetic field H^x perpendicular to the staggered field is studied by the finite-temperature density-matrix renormalization-group method. The uniform and staggered magnetization and specific heat are calculated from zero temperature to high temperatures up to T/J=4 under various strength of magnetic fields from H^y_s/J, H^x/J=0 to 2.4. The specific heat and magnetization of the effective Hamiltonian of the Yb_4As_3 are also presented, and field induced gap formation and diverging magnetic susceptibility at low temperature are shown.
Transport properties in the presence of magnetic fields are numerically studied for the spin-1/2 Heisenberg XXZ chain. The breakdown of the spin-reversal symmetry due to the magnetic field induces the magnetothermal effect. In analogy with the thermoelectric effect in electron systems, the thermomagnetic power (magnetic Seebeck coefficient) is provided, and is numerically evaluated by the exact diagonalization for wide ranges of temperatures and various magnetic fields. For the antiferromagnetic regime, we find the magnetic Seebeck coefficient changes sign at certain temperatures, which is interpreted as an effect of strong correlations. We also compute the thermomagnetic figure of merit determining the efficiency of the thermomagnetic devices for cooling or power generation.