On the Symmetry Foundation of Double Soft Theorems

Double-soft theorems, like its single-soft counterparts, arises from the underlying symmetry principles that constrain the interactions of massless particles. While single soft theorems can be derived in a non-perturbative fashion by employing current algebras, recent attempts of extending such an approach to known double soft theorems has been met with difficulties. In this work, we have traced the difficulty to two inequivalent expansion schemes, depending on whether the soft limit is taken asymmetrically or symmetrically, which we denote as type A and B respectively. We show that soft-behaviour for type A scheme can simply be derived from single soft theorems, and are thus non-preturbatively protected. For type B, the information of the four-point vertex is required to determine the corresponding soft theorems, and thus are in general not protected. This argument can be readily extended to general multi-soft theorems. We also ask whether unitarity can be emergent from locality together with the two kinds of soft theorems, which has not been fully investigated before.Comment: 45 pages, 7 figure

Topological Anderson Insulator

Disorder plays an important role in two dimensions, and is responsible for striking phenomena such as metal insulator transition and the integral and fractional quantum Hall effects. In this paper, we investigate the role of disorder in the context of the recently discovered topological insulator, which possesses a pair of helical edge states with opposing spins moving in opposite directions and exhibits the phenomenon of quantum spin Hall effect. We predict an unexpected and nontrivial quantum phase termed "topological Anderson insulator," which is obtained by introducing impurities in a two-dimensional metal; here disorder not only causes metal insulator transition, as anticipated, but is fundamentally responsible for creating extended edge states. We determine the phase diagram of the topological Anderson insulator and outline its experimental consequences.Comment: 4 pages, 4 figure