Diffusive Transport in Spin-1 Chains at High Temperatures

Abstract

We present a numerical study on the spin and thermal conductivities of the spin-1 Heisenberg chain in the high temperature limit, in particular of the Drude weight contribution and frequency dependence. We use the Exact Diagonalization and the recently developed microcanonical Lanczos method; it allows us a finite size scaling analysis by the study of significantly larger lattices. This work, pointing to a diffusive rather than ballistic behavior is discussed with respect to other recent theoretical and experimental studies. Introduction.-Recently, numerous experiments on quasi-one dimensional (1D) spin-1/2 compounds [1, 2, 3, 4, 5] have confirmed highly anisotropic thermal transport along the direction of the magnetic chains and a large contribution to the thermal conductivity due to the magnetic interactions. This is in agreement with early theoretical proposals [6,7] of ballistic transport in spin-1/2 Heisenberg antiferromagnetic chains (HAFM), that was recently related to the integrability of this system [8,9,10,11]. These developments promoted the theoretical study of several models, as spin-1/2 frustrated chains, ladders and higher spin systems, using numerical methods [12,13,14] or low energy effective theories [15,16,17,18,19].

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

“…The choice of H that determines whether the system is in the gapped or gapless phase does not seem to affect this scaling. Yet, a finite value of D QQ in the thermodynamic limit is one of the features of integrable systems [35], which is clearly not the case of the considered model (1) [1,34]. One of the possible explanations of this phenomenon is that the intrinsic diffusive processes at low T , that will result in a zero D QQ in the thermodynamic limit, become effective beyond the reachable system size or the energy resolution of the method presented here.…”

“…Moreover, for H ≥ J the ω ∼ 0 contributions are dominant in the total sum rule I QQ (ω = ∞) and almost all weight is in Drude weight itself. Since the model (1) is a nonintegrable, one would expect that D QQ is vanishing exponentially fast (at least for T → ∞) with system size L, leading to diffusive transport in the thermodynamic limit [1,34]. In order to clarify this, we present in Fig.…”

Low-temperature heat transport of spin-gapped quantum magnets

“…On the one hand, the spin-1/2 ladder is believed to have the essentially same as the spin-1 chain in the aspects of the spin-liquid ground state and the gapped magnetic spectrum. The pioneer theoretical result indicated a diffusive spin transport of the spin-1 chain system, which is a non-integrable model [52]. On the other hand, some recent theories also suggested a more complicated spin transport behavior in spin-1/2 ladders [53][54][55][56][57].…”

“…However, theoretical studies on the thermal conductivity of spin-1/2 ladders are rather controversial [52][53][54][55][56][57]. On the one hand, the spin-1/2 ladder is believed to have the essentially same as the spin-1 chain in the aspects of the spin-liquid ground state and the gapped magnetic spectrum.…”

Microcanonical Lanczos method

“…The next system we studied [10] is the spin-1 isotropic Heisenberg chain, a non-integrable model. The high temperature spin conductivity is shown in Fig.…”