Abstract
A technique to perform real-time quantum propagation of many-particle systems on finite lattices is presented and applied to the motion of a single hole in the Heisenberg and Ising magnets (t-J and t- models) for finite two-dimensional lattices of sizes 3×3 and 4×4. Use of Trotter’s formula together with a checkerboard decomposition allows a direct real-time calculation of the many-fermion dynamics to be made for asymptotically long times. Starting from localized initial states, the hole-density distribution in the single-hole system is evaluated as a function of time. We find statistical behavior already appears in the 4×4 lattice due to the large Hilbert space of the fermion background (≊ states). For J≪t, the hole appears to move almost incoherently in both models, with small quantum fluctuations. For larger values of the spin coupling J, the t- model shows a strong tendency to localize, while incorporation of the Heisenberg spin-flip term removes this feature and introduces an increasing component of low-frequency coherent motion for larger J.
- Received 1 November 1990
DOI:https://doi.org/10.1103/PhysRevB.43.11062
©1991 American Physical Society