It's not by concentration, but by attempting to copy this "magic trick" through means psychic, scientific, and frankly mental. When he finally succeeds – in the very first few pages of the novel – this mechanism gets developed further into some sort of anti-gravity drive, and the inhabitants of Earth scatter around the universe. That's where the short introduction ends; the main story picks up several hundreds of years later, when Earth has recovered from this, and starts sending around large military ships to distribute "ambassadors".
This is The Great Explosion by Eric Frank Russell (1962), a novel length version of his earlier story ... And then there were none from 1951. The short story only deals with a single of these encounters; the novel details a few more, and "... And then there were none" is where the enterprise of this particular ship effectively ends, as virtually all military and civilian personnel abandon the ship on an Utopian planet.
A relevant excerpt from the Prologue:
Four hours per day, four days per week, he sat at an office desk. The rest of his time was devoted wholly and with appalling single-mindedness to the task of levitating a penny. Wealth or power or shapely women had no appeal to him. Except when hunting a handkerchief his entire life was dedicated to what he deemed the ultimate triumph, namely, that of being able to exhibit a coin floating in mid-air.