A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
arXiv:0812.4252 · doi:10.1103/PhysRevB.79.214409
Abstract
Using the adaptive time-dependent density matrix renormalization group method, we numerically study the spin dynamics and transport in one-dimensional spin-1/2 systems at zero temperature. Instead of computing transport coefficients from linear response theory, we study the real-time evolution of the magnetization starting from spatially inhomogeneous initial states. In particular, we are able to analyze systems far away from equilibrium with this set-up. By computing the time-dependence of the variance of the magnetization, we can distinguish diffusive from ballistic regimes, depending on model parameters. For the example of the anisotropic spin-1/2 chain and at half filling, we find the expected ballistic behavior in the easy-plane phase, while in the massive regime the dynamics of the magnetization is diffusive. Our approach allows us to tune the deviation of the initial state from the ground state and the qualitative behavior of the dynamics turns out to be valid even for highly perturbed initial states in the case of easy-plane exchange anisotropies. We further cover two examples of nonintegrable models, the frustrated chain and the two-leg spin ladder, and we encounter diffusive transport in all massive phases. In the former system, our results indicate ballistic behavior in the critical phase. We discuss our findings in view of experiments on quasi-one dimensional quantum magnets and we propose that the study of the time-dependence of the spatial variance of particle densities could be instrumental in the characterization of the expansion of ultracold atoms in optical lattices as well.
12 pages Revtex4, 17 eps figures, version as published, minor revisions
References in corpus (15)
- Real time evolution using the density matrix renormalization group
- Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
- Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
- Heat conduction in low-dimensional quantum magnets
- Fermionization in an expanding 1D gas of hard-core bosons
- Thermal conductivity via magnetic excitations in spin-chain materials
- Emergence of quasi-condensates of hard-core bosons at finite momentum
- Thermal transport of the XXZ chain in a magnetic field
- Negative differential conductivity in far-from-equilibrium quantum spin chains
- Ground-state reference systems for expanding correlated fermions in one dimension
- Drude weight in systems with open boundary conditions
- Heat Transport in Quantum Spin Chains: Stochastic Baths vs Quantum Trajectories
- Quantum Fluctuations of Chirality in One-Dimensional Spin-1/2 Multiferroics: Gapless Dielectric Response from Phasons and Chiral Solitons
- Comment on "Anomalous Thermal Conductivity of Frustrated Heisenberg Spin Chains and Ladders"
- Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices