Time-dependent local Green's operator and its applications to manganites

TL;DR

This paper introduces an efficient algorithm for calculating the time-dependent local Green's operator in manganites, enabling large-scale simulations that reveal complex phase diagrams consistent with experimental observations.

Contribution

The authors develop a scalable, parallelizable algorithm for local Green's functions in manganites, outperforming exact diagonalization for large clusters and enabling detailed phase diagram studies.

Findings

Identified sequence of ground states: FM, AF-A, CE, dimer, AF-G.

Algorithm scales as N^1.55, outperforming ED for clusters >64 sites.

Results agree with experimental phase diagrams of manganites.

Abstract

An algorithm is presented to calculate the electronic local time-dependent Green's operator for manganites-related hamiltonians. This algorithm is proved to scale with the number of states $N$ in the Hilbert-space to the 1.55 power, is able of parallel implementation, and outperforms computationally the Exact Diagonalization (ED) method for clusters larger than 64 sites (using parallelization). This method together with the Monte Carlo (MC) technique is used to derive new results for the manganites phase diagram for the spatial dimension D=3 and half-filling on a 12x12x12 cluster (3456 orbitals). We obtain as a function of an insulating parameter, the sequence of ground states given by: ferromagnetic (FM), antiferromagnetic AF-type A, AF-type CE, dimer and AF-type G, which are in remarkable agreement with experimental results.