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arXiv:1304.2171 · Physical Review B

Magnetization transport in spin ladders and next-nearest-neighbor chains

Marko Žnidarič

Published Nov 25, 2013• 30 citations
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Abstract

We study magnetization transport at infinite temperature in several spin ladder systems as well as in next-nearest-neighbor coupled spin chains. In the integrable ladder considered we analytically show that the transport is ballistic in sectors with nonzero average magnetization, while numerical simulations of a nonequilibrium stationary setting indicate an anomalous transport in the zero-magnetization sector. For other systems, isotropic Heisenberg ladder and spin chains, showing eigenlevel repulsion typical of quantum chaotic systems, numerical simulations indicate diffusive transport.

DOI
10.1103/physrevb.88.205135

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We study magnetization transport at infinite temperature in several spin ladder systems as well as in next-nearest-neighbor coupled spin chains. In the integrable ladder considered we analytically show that the transport is ballistic in sectors with nonzero average magnetization, while numerical simulations of a nonequilibrium stationary setting indicate an anomalous transport in the zero-magnetization sector. For other systems, isotropic Heisenberg ladder and spin chains, showing eigenlevel repulsion typical of quantum chaotic systems, numerical simulations indicate diffusive transport.
We study transport of local magnetization in spin-1/2 Heisenberg chains in integrable and chaotic regimes at zero temperature. A clean Heisenberg chain with only nearest-neighbor interactions is integrable, whereas the addition of frustrating next-nearest neighbor interactions or yet of on-site disorder may lead to the onset of chaos. For a particular initial state far from equilibrium, the dynamics of local magnetization in the chaotic and non-chaotic clean chains is surprisingly similar, but differ significantly from the disordered system. We also discuss how quantum control methods consisting of sequences of magnetic pulses may be used to remove the effects of particular terms of the Hamiltonian, such as defects or unwanted interactions, and therefore induce a desired transport behavior.
We analyze transport of local magnetization and develop schemes to control transport behavior in finite spin-1/2 Heisenberg chains and spin-1/2 Heisenberg two-leg ladders at zero temperature. By adjusting parameters in the Hamiltonians, these quantum systems may show both integrable and chaotic limits. We provide examples of chaotic systems leading to diffusive and to ballistic transport. In addition, methods of coherent quantum control to induce a transition from diffusive to ballistic transport are proposed.
The anomalous spin diffusion of the integrable easy-axis Heisenberg chain originates in the ballistic transport of symmetry sectors with nonzero magnetization. Ballistic transport is replaced by normal dissipative transport in all magnetization sectors upon introducing the integrability-breaking perturbations, including external driving. Such behavior implies that the diffusion constant obtained for the integrable model is relevant for the spread of spin excitations but not for the spin conductivity. We present numerical results for closed systems and driven open systems, indicating that the diffusion constant shows a discontinuous variation as the function of perturbation strength.
We study transport of local magnetization in a Heisenberg spin-1/2 chain at zero temperature. The system is initially prepared in a highly excited pure state far from equilibrium and its evolution is analyzed via exact diagonalization. Integrable and nonintegrable regimes are obtained by adjusting the parameters of the Hamiltonian, which allows for the comparison of transport behaviors in both limits. In the presence of nearest-neighbor interactions only, the transport behavior in the integrable clean system contrasts with the chaotic chain with on-site defects, oscillations in the first suggesting ballistic transport, and a fast decay in the latter indicating diffusive transport. The results for a nonintegrable system with frustration are less conclusive, similarities with the integrable chain being verified. We also show how methods of quantum control may be applied to chaotic systems to induce a desired transport behavior, such as that of an integrable system.
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We show that in a nonintegrable spin ladder system with the XX type of coupling along the legs and the XXZ type along the rungs there are invariant subspaces that support ballistic magnetization transport. In the complementary subspace the transport is found to be diffusive. This shows that (i) quantum chaotic systems can possess ballistic subspaces, and (ii) diffusive and ballistic transport modes can coexist in a rather simple nonintegrable model. In the limit of an infinite anisotropy in rungs the system studied is equivalent to the one-dimensional Hubbard model.