Alex Rasmussen

Bridging fermionic and bosonic short range entangled states

In this paper we construct bosonic short range entangled (SRE) states in all spatial dimensions by coupling a

Gapless Topological Order, Gravity, and Black Holes

Z_2

Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models

gauge field to fermionic SRE states with the same symmetries, and driving the

Wave Function and Strange Correlator of Short Range Entangled states

Z_2

Stable Gapless Bose Liquid Phases without any Symmetry

gauge field to its confined phase. We demonstrate that this approach allows us to construct many examples of bosonic SRE states, and we demonstrate that the previous descriptions of bosonic SRE states such as the semiclassical nonlinear sigma model field theory and the Chern-Simons field theory can all be derived using the fermionic SRE states.

Line defects in three-dimensional symmetry-protected topological phases

In this work we demonstrate that linearized gravity exhibits gapless topological order with an extensive ground state degeneracy. This phenomenon is closely related both to the topological order of the pyrochlore U(1) spin liquid and to recent work by Hawking et. al. who used the soft photon and graviton theorems to demonstrate that the vacuum in linearized gravity is not unique. We first consider lattice models whose low-energy behavior are described by electromagnetism and linearized gravity, and then argue that the topological nature of these models carries over into the continuum. We demonstrate that these models can have many ground states without making assumptions about the topology of spacetime or about the high-energy nature of the theory, and show that the infinite family of symmetries described by Hawking et. al. are simply the difierent topological sectors. We argue that in this context black holes appear as topological defects in the IR theory, and that this suggests a potential approach to understanding both the firewall paradox and information encoding in gravitational theories. Finally, we use insights from the soft boson theorems to make connections between deconfined gauge theories with continuous gauge groups and gapless topological order.