Improved numerical methods for infinite spin chains with long-range interactions

Abstract

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 investigate some more general methods to speed up calculations and improve convergence, which might be partially interesting in a much broader context, too. As a more special problem, we also look into translational invariant states close to an invariance braking phase transition and show how to avoid convergence into wrong local minima for such systems. Finally, we apply the new methods to polar bosons with long-range interactions. We calculate several detailed Devil's Staircases with the corresponding phase diagrams and investigate some supersolid properties.

Main text: 17 pages plus references, 8 figures. Supplementary info: 6 pages. v2: improved presentation and more results added

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Cited by in corpus (5)

• Kitaev chains with long-range pairing
• Topological phases in ultracold polar-molecule quantum magnets
• Random transverse-field Ising chain with long-range interactions
• Structured Chaos in a Devil's Staircase of the Josephson Junction
• Phase-transitions of the random bond Potts chain with long-range interactions