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arXiv:cond-mat/0201392 · Journal of the Physical Society of Japan

Enhancement of the Thermal Conductivity in Gapped Quantum Spin Chains

Keiji Saito, Seiji Miyashita

Published Oct 15, 2002• 33 citations
arXivHTMLPDF

Abstract

We study mechanism of magnetic energy transport, motivated by recent measurements of the thermal conductivity in low dimensional quantum magnets. We point out a possible mechanism of enhancement of the thermal conductivity in gapped magnetic system, where the magnetic energy transport plays a crucial role. This mechanism gives an interpretation for the recent experiment of CuGeO_3, where the thermal conductivity depends on the crystal direction.

DOI
10.1143/jpsj.71.2485

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The anomalous thermal conductivity in spin chains observed in experiments is studied for the low-temperature regime. In the effective dynamics with most realistic perturbations, the so-called umklapp terms are irrelevant to reduce the mean free path in the energy transport at even finite temperatures. This is consistent with the large conductivities found in recent experiments. The Drude weight which is the prefactor in the divergent conductivity is calculated, and the temperature dependence is discussed.
We study the low-temperature transport properties of clean one-dimensional spin-12\frac{1}{2}21​ chains coupled to phonons. Due to the presence of approximate conservation laws, the heat current decays very slowly giving rise to an exponentially large heat conductivity, $\ensuremath{\kappa}\ensuremath{\sim}{e}^{{T}^{*}/T}.$ As a result of an interplay of umklapp scattering and spinon-phonon coupling, the characteristic energy scale T∗{T}^{*}T∗ turns out to be of order ${\ensuremath{\Theta}}_{D}/2,$ where ${\ensuremath{\Theta}}_{D}$ is the Debye energy, rather than the magnetic exchange interaction JJJ---in agreement with recent measurements in SrCuO compounds. A large magnetic field h strongly affects the heat transport by two distinct mechanisms. First, it induces a linear spinon-phonon coupling, which alters the nature of the $\stackrel{\ensuremath{\rightarrow}}{T}0$ fixed point: the elementary excitations of the system are composite spinon-phonon objects. Second, the change of the magnetization and the corresponding change of the wave vector of the spinons strongly affects the way in which various umklapp processes can relax the heat current, leading to a characteristic fractal-like spiky behavior of $\ensuremath{\kappa}(T,h)$ as a function of h.
We present an exact theory that describes how magnetic impurities change the behavior of the thermal conductivity for the integrable Heisenberg antiferromagnetic quantum spin-1/2 chain. Single magnetic impurities and a large concentration of impurities with similar values of the couplings to the host chain (a weak disorder) do not change the linear-in-temperature low-T behavior of the thermal conductivity: Only the slope of that behavior becomes smaller, compared to the homogeneous case. The strong disorder in the distribution of the impurity-host couplings produces more rapid temperature growth of the thermal conductivity, compared to the linear-in-T dependence of the homogeneous chain and the chain with weak disorder. Recent experiments on the thermal conductivity in inhomogeneous quasi-one-dimensional quantum spin systems manifest qualitative agreement with our results.
The transport properties of quantum systems are one of the most interesting current topics in statistical physics. Heat transport can directly be observed through thermal conductivity measurements, while spin transport can be extracted from nuclear spin–lattice relaxation-time measurements. Numerous experiments have indeed been performed in an attempt to settle the argument about whether finite-temperature energy transport should be diffusive or ballistic. From the theoretical point of view, there is an argument that integrable Hamiltonians exhibit ballistic transport, whereas nonintegrable ones are diffusive or insulators. Since nonintegrable systems have much less been studied in this context so far, we investigate spin-½ ferromagnetic-antiferromagnetic bond-alternating chains, which exhibit common features of Haldane-gap antiferromagnets. Employing the Jordan–Wigner spinless-fermion representation, their level statistics is investigated by the exact-diagonalization method. We argue a possibility of the diffusive transport occurring in the system.