Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model
Date
1997-06-05
DOI
Authors
Campbell, David K.
Singh, R. R. P.
Sandvik, A. W.
Version
OA Version
Citation
1997. "Quantum Monte Carlo in the Interaction Representation ---
Application to a Spin-Peierls Model," cond-mat/9706046.
http://arxiv.org/abs/cond-mat/9706046
Abstract
A quantum Monte Carlo algorithm is constructed starting from the
standard perturbation expansion in the interaction representation. The resulting
configuration space is strongly related to that of the Stochastic Series Expansion (SSE)
method, which is based on a direct power series expansion of exp(-beta*H). Sampling
procedures previously developed for the SSE method can therefore be used also in the
interaction representation formulation. The new method is first tested on the S=1/2
Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg
chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the
spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is
implemented in the phonon occupation number basis, without Hilbert space truncations, and is
exact. Results are presented for the magnetic properties of the system in a wide temperature
regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some
aspects of the phonon dynamics are also discussed. The results suggest that the effects of
dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in
order to obtain a correct quantitative description of their magnetic properties, both above
and below the dimerization temperature.