Students ... be quiet at the library.

The sentence expresses a rule or obligation in a specific place (library). 'Must' is used to express strong obligation or necessity. 'Have to' and 'has to' also express obligation but often imply an external source of the rule. 'Mustn't' expresses prohibition. Therefore, 'must' is the most appropriate choice for a general rule or strong recommendation in this context.

The correct option is: must