Quantum orders and symmetric spin liquids

A concept---quantum order---is introduced to describe a new kind of orders that generally appear in quantum states at zero temperature. Quantum orders that characterize the universality classes of quantum states (described by complex ground-state wave functions) are much richer than classical orders that characterize the universality classes of finite-temperature classical states (described by positive probability distribution functions). Landau's theory for orders and phase transitions does not apply to quantum orders since they cannot be described by broken symmetries and the associated order parameters. We introduced a mathematical object---projective symmetry group---to characterize quantum orders. With…