1205.2674 (V. Nebendahl et al.)
V. Nebendahl, W. Dür
We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed multi-optimization (SMO) method, which allows an efficient optimization of exponentially many MPS of different length at different sites all in one step. Hereby the algorithm becomes protected against position dependent effects as caused by spontaneously broken translational invariance. So far, these have been a major obstacle to convergence for the iMPS algorithm if no prior knowledge of the systems translational symmetry was accessible. Further, we show that the underlying tensor structure of the resulting iMPS offers an easy way to attain any desired solution out of a manifold of ground states if degeneration is due to broken translational invariance. Finally, we apply the new methods to polar bosons with long-range interactions and calculate some detailed Devil's Staircases and phase diagrams.
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http://arxiv.org/abs/1205.2674
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