Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
arXiv:1009.4646 · doi:10.1103/PhysRevLett.106.077202
Abstract
The numerical simulation of quantum many-body dynamics is typically limited by the linear growth of entanglement with time. Recently numerical studies have shown, however, that for 1D Bethe-integrable models the simulation of local operators in the Heisenberg picture can be efficient as the corresponding operator-space entanglement grows only logarithmically. Using the spin-1/2 XX chain as generic example of an integrabel model that can be mapped to free particles, we here provide a simple explanation for this. We show furthermore that the same reduction of complexity applies to operators that have a high-temperature auto correlation function which decays slower than exponential, i.e., with a power law. This is amongst others the case for models where the Blombergen-De Gennes conjecture of high-temperature diffusive dynamics holds. Thus efficient simulability may already be implied by a single conservation law (like that of total magnetization), as we will illustrate numerically for the spin-1 XXZ model.
4 pages, 2 figures
References in corpus (14)
- Real time evolution using the density matrix renormalization group
- Matrix product states represent ground states faithfully
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Entropy scaling and simulability by Matrix Product States
- Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
- Operator space entanglement entropy in transverse Ising chain
- General entanglement scaling laws from time evolution
- Is efficiency of classical simulations of quantum dynamics related to integrability?
- On entropy growth and the hardness of simulating time evolution
- Logarithmic current fluctuations in non-equilibrium quantum spin chains
- Operator Space Entanglement Entropy in XY Spin Chains
- Density Matrix Renormalization Group in the Heisenberg Picture
- Spin diffusion and the anisotropic spin-1/2 Heisenberg chain