Real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method

Langer, S., Heidrich-Meisner, F., Gemmer, J., McCulloch, I. P. and Schollwock, U. (2009) Real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method. Physical Review B (Condensed Matter and Materials Physics), 79 21: 214409.1-214409.11. doi:10.1103/PhysRevB.79.214409

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Author Langer, S.
Heidrich-Meisner, F.
Gemmer, J.
McCulloch, I. P.
Schollwock, U.
Title Real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
Journal name Physical Review B (Condensed Matter and Materials Physics)   Check publisher's open access policy
ISSN 1098-0121
1550-235X
Publication date 2009-06-09
Sub-type Article (original research)
DOI 10.1103/PhysRevB.79.214409
Open Access Status File (Publisher version)
Volume 79
Issue 21
Start page 214409.1
End page 214409.11
Total pages 11
Editor P. D. Adams
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2010
Language eng
Subject C1
020603 Quantum Information, Computation and Communication
970102 Expanding Knowledge in the Physical Sciences
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 setup. 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 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.
Keyword Thermal-conductivity
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Article number 214409

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
ERA 2012 Admin Only
 
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Created: Thu, 03 Sep 2009, 17:49:43 EST by Mr Andrew Martlew on behalf of Physics