Non-dissipative Thermal Transport and Magnetothermal Effect for the Spin-1/2 Heisenberg Chain

Abstract

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.KEYWORDS: transport properties, thermal conductivity, magnetothermal effect, Seebeck coefficient, Heisenberg chainIn the last two decades, 1D strongly correlated systems have attracted immense theoretical and experimental interest. One of the reasons stems from their unusual static and dynamical properties peculiar to 1D systems. The spin-1/2 Heisenberg chain is one of the most fundamental solvable models for 1D magnetic insulators and has served as a testing ground for many approaches.Recently, transport properties of low-dimensional strongly correlated quantum systems have been extensively studied from both theoretical and experimental sides.1) Among them anomalously enhanced thermal conductivity 2-4) and unconventional large spin diffusion constants 5) have been reported in experiments on one-or quasi 1D materials with weak interchain interactions. These observations indicate the existence of nondissipative transport properties in 1D quantum systems. Theoretically, the existence of such anomalous properties has also been pointed out especially in quantum integrable systems. 6) One of the criteria for anomalous transport is the existence of a non-zero Drude weight.In particular for the spin-1/2 XXZ chain, the Drude weight for the spin transport has been obtained by Zotos for finite temperature at zero magnetic field.7) In the massless regime, the Drude weight is non-zero and hence the spin transport is non-dissipative. In the massive regime without magnetic field a similar treatment yields zero Drude weight at any temperature implying dissipative spin transport. This feature, however, contradicts with numerical or field theoretical approaches and is still debated. 8-10)On the other hand, the thermal Drude weight D th (T ) for zero magnetic field has been recently obtained by the Bethe ansatz showing that the thermal transport is non-dissipative in both massless and massive regimes.11, 12) At low-temperature D th (T ) behaves as D th (T ) = πv F T /3 where v F is the velocity of excitations. This universal behavior was also found in gen- * E-mail address: sakai@stat.phys.titech.ac.jp † E-mail address: kluemper@physik.uni-wuppertal.de eral systems in which the low-energy excitations are described by a c = 1 conformal field theory. 13,14) In the massive regime, we find that D th (T ) ∼ exp(−δ/T )/ √ T where δ is the one-spinon (respectively one...

EffectiveS=12description of theS=1chain with strong easy-plane anisotropy

“…Such a term originates from the coupling of the heat and spin currents in the presence of magnetic field [32,31,33]. Here we present results for the heat conductivity κ QQ (ω) calculated for S = 1 model with FTLM on the chain up to L = 16 sites and exact results obtained for S = 1/2 model.…”

“…(10), with r = 1 for i = j = Q or i = j = E, and r = 0 for i = j = S or i = E, j = S. The D EE and D ES at finite temperatures have been calculated by Sakai and Klümper [31] using a lattice path integral formulation, where a quantum transfer matrix (QTM) in the imaginary time is introduced. Correlations and thermodynamic quantities can be evaluated in terms of the largest eigenvalue of the QTM.…”

Conservation laws, integrability, and transport in one-dimensional quantum systems

“…To do so we computed the equal time correlations using a numerical solution of the nonlinear integral equations obtained within the Bethe ansatz formalism of Refs. [61,62]. In Fig.…”

Spin and magnetothermal transport in theS = 1/2 XXZ chain

“…In the case of insulators the study of thermal transport as a function of magnetic field is particularly attractive, as the magnetic field provides a handle to separate the field-independent phononic contribution from the total measured thermal conductivity [3], confronting subtle theoretical analysis to experiments. Furthermore, several intriguing phenomena in which the interplay of spin and heat transport play a crucial role have been suggested [6][7][8][9]. In analogy to the thermoelectric effect in electronic conductors a spin -Seebeck effect should arise in the presence of a temperature gradient in electronic insulators.…”

“…The knowledge of D ss (T, H) also al- lows for the calculation of the thermal Drude weight K th and intriguing magnetothermal phenomena that arise due to the coupling of the energy and spin currents [6]. Theoretically the problem of transport in the Heisenberg S = 1/2 chain has been adressed by mean-field methods plus relaxation time approximation [22] and a combination of numerical exact diagonalization as well as Bethe ansatz techniques [7,8].…”