New Phases of Matter: Topological Physics in the 21^st Century

One of the fundamental problems in theoretical physics is the classification of phases of matter. A successful theory on this front was pioneered by the physicist Landau, who proposed a theory of phase transition based on spontaneous symmetry breaking. Since then, however, other kinds of phases have emerged that cannot be characterized by spontaneous symmetry breaking.

A now well-known example of such phases is the topological phases. These are gapped phases that appear at absolute zero temperature without breaking symmetry. They have been observed in fractional quantum Hall systems and in the manifestation of anyons, quasiparticles that are neither bosons nor fermions.

In view of this, a recent editorial by researchers from Japan provides an overview of our current understanding of topological phases and their relevance in physics.

Among various topological states, a new type of state called “symmetry protected topological phase” or SPT phase has been identified in Modern physics of the 21st century. These are states that do not have a ground state degeneracy and yet are non-trivial. A well-known example of SPT phases comes from topological insulators, materials that show metallic surface states that are robust against disorder effects that do not break the symmetry.

One way to characterize such surface states is through quantum anomalies. The quantum anomaly only arises when confined to the surface and disappears when the whole system is considered. This is due to cancellations that arise from bulk contribution. Thus, the classification of SPT phases can be achieved through the classification of quantum anomaly via the bulk-boundary correspondence.

The concept of topological phases is of importance in several areas of physics, such as particle physics, condensed matter physics, and statistical mechanics. It can not only provide us insights into new physics at low temperatures but can also help us in our quest towards realizing quantum computers.