What caused the split with the Roman Catholic Church during the eleventh century?

Answer 1

Some people thought that worshiping idols (such as a statue) was wrong, but others thought that it was ok. So they performed a schism (a split).

Roman Catholic AnswerMany things, mostly based on sin, in other words, men wanting to do their own will, and not the will of God:

from A Catholic Dictionary, edited by Donald Attwater, Second edition, revised 1957

The Schism of the East the estrangement and severance from the Holy See of what is now called the Orthodox Eastern Church was a gradual process extending over centuries. After a number of minor schisms the first serious, though short, break was that of Photius; from then on tension between East and West increased, and the schism of Cerularius occurred in 1054. From then on the breach gradually widened and has been definitive since 1472. There was a formal union from the 2nd Council of Lyons in 1274 until 1282, and a more promising one after the Council of Florence from 1439 to 1472. After the capture of Constantinople it was in the Turkish interest to reopen and widen the breach with the powerful Roman church; the patriarchates of Alexandria, Antioch, and Jerusalem were dragged into this policy, Russia and the Slav churches stood out the longest of any: none of these churches, except Constantinople itself in 1472, formally and definitely broke away from the unity of the Church. But in the course of centuries the schism has set and crystallized into a definite separation from the Holy See of many million people with a true priesthood and valid sacraments. The origins, causes and development of the schism are matters of much complication, still not fully unraveled.

Answer 2

Between the Eastern Church centered in Byzantium, and the Western Church centered in Rome.