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arXiv:1005.0199 · Physical Review B

Field-dependent spin and heat conductivities of dimerized spin- 12 chains

S. Langer, R. Darradi, Fabian Heidrich‐Meisner, W. Brenig

Published Sep 20, 2010• 12 citations
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Abstract

We study the spin and heat conductivity of dimerized spin-$\frac{1}{2}$ chains in homogeneous magnetic fields at finite temperatures. At zero temperature, the model undergoes two field-induced quantum phase transitions from a dimerized, into a Luttinger, and finally into a fully polarized phase. We search for signatures of these transitions in the spin and heat conductivities. Using exact diagonalization, we calculate the Drude weights, the frequency dependence of the conductivities, and the corresponding integrated spectral weights. As a main result, we demonstrate that both the spin and heat conductivity are enhanced in the gapless phase and most notably at low frequencies. In the case of the thermal conductivity, however, the field-induced increase seen in the bare transport coefficients is suppressed by magnetothermal effects, caused by the coupling of the heat and spin current in finite magnetic fields. Our results complement recent magnetic transport experiments on spin-ladder materials with sufficiently small exchange couplings allowing access to the field-induced transitions.

DOI
10.1103/physrevb.82.104424

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We study the spin and thermal conductivity of spin-12\frac{1}{2}21​ ladders and chains at finite temperature, relevant for experiments with quantum magnets. Using a state-of-the-art density matrix renormalization group algorithm, we compute the current autocorrelation functions on the real-time axis and then carry out a Fourier integral to extract the frequency dependence of the corresponding conductivities. The finite-time error is analyzed carefully. We first investigate the limiting case of spin-12\frac{1}{2}21​ XXZXXZXXZ chains, for which our analysis suggests nonzero dc conductivities in all interacting cases irrespective of the presence or absence of spin Drude weights. For ladders, we observe that all models studied are normal conductors with no ballistic contribution. Nonetheless, only the high-temperature spin conductivity of XXXXXX ladders has a simple diffusive, Drude-like form, while Heisenberg ladders exhibit a more complicated low-frequency behavior. We compute the dc spin conductivity down to temperatures of the order of $T\ensuremath{\sim}0.5J$, where JJJ is the exchange coupling along the legs of the ladder. We further extract mean-free paths and discuss our results in relation to thermal conductivity measurements on quantum magnets.
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