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

TL;DR

This paper introduces an improved iMPS algorithm with the superposed multi-optimization method for efficiently finding ground states of 1D quantum systems with long-range interactions, overcoming previous convergence issues.

Contribution

The paper presents the superposed multi-optimization method, enabling efficient optimization of multiple MPS and addressing translational symmetry breaking in long-range interacting systems.

Findings

Successfully applied to polar bosons with long-range interactions

Generated detailed phase diagrams and Devil's Staircases

Enhanced convergence and avoided local minima in complex systems

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.