Cenke Xu

One of the main goals of condensed matter theory is to understand the ground state of strongly interacting quantum quantums. We can very roughly classify the ground states of strongly interacting quantum systems into two categories: (1), semiclassical states; and (2), exotic states. Semiclassical states refer to systems that can be described using the similar formalism as classical systems, for instance using the Landau order parameter and Landau-Ginzburg theory. Many concepts and nontions in classical physics are proved useful (if not sufficient) in describing semiclassical quantum states, for instance the spontaneous symmetry breaking, Goldstone modes et.al..

To describe the semiclassical states more quantitatively, one can start with the classical limit, and turn on quantum fluctuations order by order systematically. For instance, in quantum magnet the classical limit is the large S limit, where the spin has infinite quantization direction in space, and hence equivalent to classical spins. Then one can turn on quantum flucuation by 1/S expansion. However, usually the 1/S expansion does not change the ground states qualitatively, except for lifting the accidental degeneracy of ground states in the classical limit.

Exotic states usually refer to ground states of strongly correlated systems that do not have classical counterparts, therefore all the techniques starting from the classical limit fail in principle. Unlike semiclassical states, the exotic states usually cannot be described by local Landau order parameters. In order to describe exotic states, people have developed new language and concepts, like spin liquid, topological order , string-net condensation et.al.

More coming later......