Exact time-dependent propagation of vacancy motion in the t-J limit of the two-dimensional Hubbard Hamiltonian

Qing Zhang and K. Birgitta Whaley
Phys. Rev. B 43, 11062 – Published 1 May 1991
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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-Jz 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 (≊105 states). For Jt, the hole appears to move almost incoherently in both models, with small quantum fluctuations. For larger values of the spin coupling J, the t-Jz 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

Authors & Affiliations

Qing Zhang and K. Birgitta Whaley

  • Department of Chemistry, University of California at Berkeley, Berkeley, California 94720

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Issue

Vol. 43, Iss. 13 — 1 May 1991

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