How to turn off screen with shortcut in Linux?

Problem

Since my monitor takes an awful lot of time to turn back on after being physically turned off, I'm looking for a command or a simple utility to turn off my screen with a shortcut. Setting a black screensaver is not satisfactory; I want the screen to "hibernate" (the same effect I would get by turning off the computer while leaving the screen physically on). The same question for Windows: How can I make my screen blank by a shortcut?