Spin and energy currents in integrable and nonintegrable spin-1/2 chains: A typicality approach to real-time autocorrelations

Abstract

We use the concept of typicality to study the real-time dynamics of spin and energy currents in spin-1/2 models in one dimension and at nonzero temperatures. These chains are the integrable XXZ chain and a nonintegrable modification due to the presence of a staggered magnetic field oriented in z direction. In the framework of linear response theory, we numerically calculate autocorrelation functions by propagating a single pure state, drawn at random as a typical representative of the full statistical ensemble. By comparing to small-system data from exact diagonalization (ED) and existing short-time data from time-dependent density matrix renormalization group (tDMRG), we show that typicality is satisfied in finite systems over a wide range of temperature and is fulfilled in both, integrable and nonintegrable systems. For the integrable case, we calculate the long-time dynamics of the spin current and extract the spin Drude weight for large systems outside the range of ED. We particularly provide strong evidence that the high-temperature Drude weight vanishes at the isotropic point. For the nonintegrable case, we obtain the full relaxation curve of the energy current and determine the heat conductivity as a function of magnetic field, exchange anisotropy, and temperature.

14 pages, 14 figures, accepted for publication in Phys. Rev. B

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Cited by in corpus (8)

• Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
• Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• A class of states supporting diffusive spin dynamics in the isotropic Heisenberg model
• Coexistence of diffusive and ballistic transport in integrable quantum lattice models
• Temperature Dependent Energy Diffusion in Chaotic Spin Chains
• Non-equilibrium thermal transport and vacuum expansion in the Hubbard model
• Energy dynamics in a generalized compass chain