Condensed Matter and Biological Physics Seminars

In recent years, a new paradigm of "topological quantum order" (TQO) has emerged. These orders cannot be characterized by local quantities and have led to a wealth of ideas and results motivated, in part, by the prospect of fault tolerant quantum computing. Here, we will show that all known examples of topological quantum order harbor a symmetry which generally lies midway between local symmetries (that of gauge theories) and global symmetries (as in most condensed matter systems). Apart from the prominent examples of TQO, these symmetries also appear in orbital models, some frustrated magnets, cold atoms systems and Josephson junction systems. We will show how these symmetries can mandate TQO. We will further show that by duality transformations, many of these systems can be mapped onto systems with global symmetries (and orders). These mappings allow us to assess the effect of finite temperatures. We will conclude with an exact solution to a nearest neighbor pyrochlore antiferromagnet in which some of these notions are clearly fleshed out and their relation to an exact quantum criticality is elucidated.